UrbanPro

Location Set your Location

Login Ask & Answer Success Stories Paid Courses Free Classes Tuition & Classes Fees Write a Review All Categories Help Center
Post your Learning Need Signup as a Tutor
✕

Popular Cities

Bangalore

Hyderabad

Delhi

Mumbai

Chennai

Pune

Kolkata

Gurgaon

Ahmedabad

Jaipur

Noida

✕

Take Class 10 Tuition from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

Book a Free Demo

Class 10 > Learn Class IX-X Tuition > If p = 2sinA /1+cosA+sinA and q = cosA / 1+sinA ,Then...
✕

Search in

If p = 2sinA /1+cosA+sinA and q = cosA / 1+sinA ,Then prove that p+q = 1

Asked by Last Modified  

17 Answers

Learn Class IX-X Tuition

Follow 2
Answer

Please enter your answer

Computer Expert

Given that p = 2sinA /1+cosA+sinA and q = cosA / 1+sinA We have to prove p+q = 1 Proof: LHS p+q=(2sinA/1+casA+sinA) + (casA/1+sinA) ={2sinA(1+sinA) + cosA(1+casA+sinA)} / (1+sinA+casA)(1+sinA) =(2sinA+2sinAsinA + casA+casAcasA+casAsinA) / (1+sinA+casA)(1+sinA) ={2sinA+2sinAsinA...
read more
Given that p = 2sinA /1+cosA+sinA and q = cosA / 1+sinA We have to prove p+q = 1 Proof: LHS p+q=(2sinA/1+casA+sinA) + (casA/1+sinA) ={2sinA(1+sinA) + cosA(1+casA+sinA)} / (1+sinA+casA)(1+sinA) =(2sinA+2sinAsinA + casA+casAcasA+casAsinA) / (1+sinA+casA)(1+sinA) ={2sinA+2sinAsinA + casAcasA +casA(1+sinA)} / (1+sinA+casA)(1+sinA) ={2sinA+sinAsinA+1+casA(1+sinA) } / (1+sinA+casA)(1+sinA) ={sinAsinA +sinA+sinA+1 +casA(1+sinA)} / (1+sinA+casA)(1+sinA) ={sinAsinA+sinA +(sinA+1)(1+casA)} / (1+sinA+casA)(1+sinA) ={sinA(sinA+1) +(sinA+1)(casA+1)} / (1+sinA+casA)(1+sinA) ={(sinA+1)(sinA+casA+1)} / (1+sinA+casA)(1+sinA) =1 RHS Hence Proved. read less
Comments
Dislike Bookmark

B Tech ( NIT Jamshedpur)

write as SInA= 2sinA/2cosA/2, 1+cosA=2cos2A & CosA=cos2A/2-Sin2A/2
Comments
Dislike Bookmark

Tutor

1-q = / (1+sinA) multiplying numerator and denominator by (1+sinA+cosA) = / Simplifying by opening the brackets = / () = 2sinA / = p So, q+p=1 NOTE:- sinA not equal to -1
Comments
Dislike Bookmark

Math Educator for Std.11th ,12th , Engineering Entrance and Degree Level with 11+ Years Experience

p + q = 2sinA /1+ cos A + sin A + cosA / 1+ sin A = 2sinA + 2 sin2A + cos A + cos2A + cos A.sin A / (1+cos A +sin A) (1 + sinA) = (1+sinA+cosA) + (sin2A + sinA + sinA.cosA) / (1+cosA+sinA) (1+sinA) = (1+sinA+cosA)(1+sinA) / (1+sinA+cosA) (1+sinA) = 1
Comments
Dislike Bookmark

Tutor

The solution given by Shalini is the right way of solving the problem.
Comments
Dislike Bookmark

passion for teaching mathematics

p=2SineA/(1+Sine A+Cos A) q= CosA/(1+SineA) Then prove that p+q =1 We know, Sine A= 2TanA/2/(1+Tan^2 A/2), CosA= (1-Tan ^2 A/2)/(1+Tan ^2 A/2) Now, 2SineA/(1+Sine A+Cos A)= (2x2 TanA/2)/ 1+ Tan^2 A/2 ...
read more
p=2SineA/(1+Sine A+Cos A) q= CosA/(1+SineA) Then prove that p+q =1 We know, Sine A= 2TanA/2/(1+Tan^2 A/2), CosA= (1-Tan ^2 A/2)/(1+Tan ^2 A/2) Now, 2SineA/(1+Sine A+Cos A)= (2x2 TanA/2)/ 1+ Tan^2 A/2 1 +(2 TanA/2)/ 1+ Tan^2 A/2 ) +(1-Tan^2 A/2)/(1+Tan^2 A/2) P= 4TanA/2 2(1+TanA/2) = 2TanA/2 (1+TanA/2) q= CosA/(1+SineA) = (1-Tan^2 A/2)/(1+Tan ^2 A/2) 1 +(2 TanA/2)/ 1+ Tan ^2 A/2 ) = 1-TanA/2 1+TanA/2 P+q= 2TanA/2 + 1-TanA/2 (1+TanA/2) 1+TanA/2 (1+TanA/2)/(1+TanA/2)= 1 Provided A/2 �2npi-pi/2 read less
Comments
Dislike Bookmark

passion for teaching mathematics

p=2SineA/(1+Sine A+Cos A) q= CosA/(1+SineA) Then prove that p+q =1 We know, Sine A= 2TanA/2/(1+Tan2A/2), CosA= (1-Tan2A/2)/(1+Tan2A/2) Now, 2SineA/(1+Sine A+Cos A)= (2x2 TanA/2)/ 1+ Tan2A/2 1 +(2...
read more
p=2SineA/(1+Sine A+Cos A) q= CosA/(1+SineA) Then prove that p+q =1 We know, Sine A= 2TanA/2/(1+Tan2A/2), CosA= (1-Tan2A/2)/(1+Tan2A/2) Now, 2SineA/(1+Sine A+Cos A)= (2x2 TanA/2)/ 1+ Tan2A/2 1 +(2 TanA/2)/ 1+ Tan2A/2 ) +(1-Tan2A/2)/(1+Tan2A/2) P= 4TanA/2 2(1+TanA/2) = 2TanA/2 (1+TanA/2) q= CosA/(1+SineA) = (1-Tan2A/2)/(1+Tan2A/2) 1 +(2 TanA/2)/ 1+ Tan2A/2 ) = 1-TanA/2 1+TanA/2 P+q= 2TanA/2 + 1-TanA/2 (1+TanA/2) 1+TanA/2 (1+TanA/2)/(1+TanA/2)= 1 Provided A/2 ?2n?-?/2 read less
Comments
Dislike Bookmark
2sinA p is equal to Solve
Comments
Dislike Bookmark

p+q =2sinA/1+cosA +sinA +cosA/1+sinA= STEP-1=2sinA+2sin^2A+cosA+cos^2A+sinAcosA/(1+sinA+cosA)(1+sinA) STEP-2= 2sinA+1+sin^2A+cosA+sinAcosA/(1+sinA+cosA)(1+sinA) {since cos^2A=1-sin^2A} STEP-3= (sinA+cosA+1)+sinA+sin^2A+sinAcosA/(1+sinA+cosA)(1+sinA) {2sinA=sinA+sinA} STEP-4= (1+sinA+cosA)+sinA(1+sinA+cosA)/(1+sinA+cosA)(1+sinA) STEP-5=...
read more
p+q =2sinA/1+cosA +sinA +cosA/1+sinA= STEP-1=2sinA+2sin^2A+cosA+cos^2A+sinAcosA/(1+sinA+cosA)(1+sinA) STEP-2= 2sinA+1+sin^2A+cosA+sinAcosA/(1+sinA+cosA)(1+sinA) {since cos^2A=1-sin^2A} STEP-3= (sinA+cosA+1)+sinA+sin^2A+sinAcosA/(1+sinA+cosA)(1+sinA) {2sinA=sinA+sinA} STEP-4= (1+sinA+cosA)+sinA(1+sinA+cosA)/(1+sinA+cosA)(1+sinA) STEP-5= (1+sinA+cosA)(1+sinA)/(1+sinA+cosA)(1+sinA)=1 HENCE PROVED NOTE:if any doubt is there in d solution cn text me thnk u read less
Comments
Dislike Bookmark

Mathematics,Science and Core Java/Computer Private Tutor

p+q = (2sinA /1+cosA+sinA) + (CosA/1+sinA) Taking LCM of denominators we get Denominator as (1+cosA+sinA)(1+sinA) Therefore, Numerator becomes (2SinA(1+sinA) + CosA(1+cosA+sinA) =( 2SinA+2Sin^2A+CosA+Cos^2A+CosASinA) = 2SinA+Sin^2A+Sin^2A+Cos^2A+CosA+CosASinA =2SinA+Sin^2A+1+CosA+cosASinA =(SinA+1)(SinA+1)...
read more
p+q = (2sinA /1+cosA+sinA) + (CosA/1+sinA) Taking LCM of denominators we get Denominator as (1+cosA+sinA)(1+sinA) Therefore, Numerator becomes (2SinA(1+sinA) + CosA(1+cosA+sinA) =( 2SinA+2Sin^2A+CosA+Cos^2A+CosASinA) = 2SinA+Sin^2A+Sin^2A+Cos^2A+CosA+CosASinA =2SinA+Sin^2A+1+CosA+cosASinA =(SinA+1)(SinA+1) +CosA(SinA+1) =(SinA+1)(SinA+CosA+1) Numerator /Denominator = 1=> hence proved Note: Sin^2A => read as Sine square A 2Sin^2A = Sin^2A + Sin^2A Sin^2A + Cos^2A = 1 read less
Comments
Dislike Bookmark

View 15 more Answers

Related Questions

name the colour of the Betelgeuse star
Orange-red
Kumar Upendra Akshay
1 0
5
What is harmonic progression?
It is a progression formed by taking the reciprocals of an arithmatic progression.1/a,1/a+d,1/a+2d,1/a+3d,.........1/a+kd. the harmonis term means neighboring terams.
Ravi Ranjan
0 0
9
what is the organ of corti ?
a structure in the cochlea of the inner ear which produces nerve impulses in response to sound vibrations
Kumar Upendra Akshay
0 0
6
Name the axes where the two coordinate meet?
The point of intersection of the axes is called the origin.
Bimal
Which form of energy will a body possess placed at the top of hill?
Potential energy
Sandhya

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Related Lessons

Methodology of Learning - specially mathematics
tt ALWAYS TAKE THE HELP OF THE INTERNET. EXCELLENT REFERENCE MATERIAL IS AVAILABLE HERE IN PRACTICALLY EVERY SUBJECT THAT YOU CAN THINK OF. DO NOT WITH ONLY ONE SITE, GO TO AS MANY SITES AS POSSIBLE...

Sri Balaji Academy

1 0
0
Easiest way to Find the Remainder on dividing by 7
Split the digits of the number in a group of 3 starting from unit’s place. Add the alternate group and then find their difference. Divide the difference by 7 and get the remainder. Consider the...

Debraj Paul

0 0
0
Google Street View Cars Are Mapping Methane Leaks
Natural gas pipeline leaks that pose a safety hazard are quickly addressed. But what about leaks too small to pose a threat? These mall leaks are often overlooked and they collectively release tons of...

Rajesh N V

3 0
1
Number Game (Do Squares with in seconds)
Hi Students, Here its me Raksha - Maths Teacher. You know how to do square of those numbers which unit place is 5 within second? If NO, then please read below and after this you will be surely able...
R

Raksha G.

0 0
0
Essay on Make in India
Make in India Modiji our P.M. said : "The world is looking at Asia. I do not have to waste time to invite people. I need to give them the address." Make in India campaign : Make in India is the BJP-led...

Sudhansu Bhushan Roy

1 0
0

Recommended Articles

Meet Raghunandan.G.H, a B. Tech Tutor from...

Raghunandan is a passionate teacher with a decade of teaching experience. Being a skilled trainer with extensive knowledge, he provides high-quality BTech, Class 10 and Class 12 tuition classes. His methods of teaching with real-time examples makes difficult topics simple to understand. He explains every concept in-detail...

Read full article >

Quest Academy - Institute of the month

Quest Academy is a professional Bangalore based NEET and JEE (Main + Advanced) training institute. The academy was incorporated in 2015 to cater to the needs of students, who aim to crack competitive exams by connecting with the best brains around. The institute helps students enhance their skills and capabilities through...

Read full article >

Meet Swati, a Hindi Tutor from Bangalore

Swati is a renowned Hindi tutor with 7 years of experience in teaching. She conducts classes for various students ranging from class 6- class 12 and also BA students. Having pursued her education at Madras University where she did her Masters in Hindi, Swati knows her way around students. She believes that each student...

Read full article >

Meet Mohammad Wazid, a skilled trainer for...

Mohammad Wazid is a certified professional tutor for class 11 students. He has 6 years of teaching experience which he couples with an energetic attitude and a vision of making any subject easy for the students. Over the years he has developed skills with a capability of understanding the requirements of the students. This...

Read full article >

Find Class 10 Tuition near you
Class 10 Tuition in Delhi
Class 10 Tuition in Bangalore
Class 10 Tuition in Hyderabad
Class 10 Tuition in Kolkata
Class 10 Tuition in Mumbai
Class 10 Tuition in Chennai
Class 10 Tuition in Pune
Class 10 Tuition in Noida
Class 10 Tuition in Lucknow
Class 10 Tuition in Jaipur

Looking for Class 10 Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you
X

Looking for Class 10 Tuition Classes?

The best tutors for Class 10 Tuition Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Class 10 Tuition with the Best Tutors

The best Tutors for Class 10 Tuition Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more

ThinkVidya Learning Pvt Ltd © 2010-2024All Rights Reserved