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

Asked by Last Modified  

17 Answers

Follow 2
Answer

Please enter your answer

Krishna Kumar

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

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

Teaching is my passion!!!!

p+q=(2sin A)/(1+sinA+cosA) +((cosA/1+sinA))..........TAKE LCM AND MULTIPLY D VALUE IN NUMERATOR AND DENOMINATOR.......D NUMERATOR AND DENOMINATOR WILL COME SAME...AND HENCE 1
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

B Tech ( NIT Jamshedpur)

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

Headstart to assured 95+ score in math

Yes
Comments
Dislike Bookmark

Yes
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

Tutor

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

View 15 more Answers

Related Questions

What is Biodiversity?
The term biodiversity refers to the variety of life on Earth at all its levels, from genes to ecosystems, and the ecological and evolutionary processes that sustain it. Biodiversity includes not only species...
Dr. Anshu
Define monsoons. What do you understand by “break” in monsoon?
The wind that is from the south region and south-east Asia that blows from the month of May to September, which brings rain can be called as monsoon rain. It is a seasonal shift that brings torrential...
Vaibhav
0 0
7
Define parallax error?
It is due to the wrong displacement of the eye during reading measurement.
My
0 0
8
Why is respiration considered an exothermic reaction? Explain.
Carbohydrates present in food are broken down to form glucose. This glucose combines with Oxygen in the cells of our body and provides energy. This reaction is known as respiration. Hence, respiration is considered as an exothermic reaction.
Nandhini
0 0
5
How do you know that a state or a country is economically developed?
GNP AND GDP are the criteria for deciding the economic health of the country or state.
Amanbir

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

Ask a Question

Related Lessons

Lessons On Motion Numerical Problems.
The basic identities related to speed, velocity, accleration numerical problems are: V = u+at a = V-U/t S = ut+1/at2 2as = v2-u2 The first identity is followed when the intial velocity, acceleration...

Soumi R.

3 0
0
Rational Numbers
A number of the form p/q where q not equals to zero is called a rational numbers. P may be zero or may not. P and q are positive /negative integers. It denotes the part of a quantity...
M

Mohit S.

1 0
0
Types of electric lights Tungsten filament bulbs Neon lights Fluorescent tubes
Electric lights are now used every day and night as an artificial form of light. There are several different types of electric lights including tungsten filament light bulbs, neon lights and fluorescent...

Debraj Paul

0 0
0
CONCEPTUAL CLARITY
WHILE STUDYING ANY TOPIC MAKE SURE THAT AVOID MULTIPLE SOURCES. INSTEAD PICK UP ONE STANDARD SOURCE AND THE CONTENT OF WHICH YOU CAN COMPREHEND. READ IT MULTIPLE TIMES...FRAME A PICTURE IN MIND....ANALYSE...

Nimesh Singhvi

4 0
0
How To Learn French Language In Easy Way?
Step 1: Fall in Love with French: What’s the key to speaking French? Passion. French is the language of love. And to speak any language, you’ve got to fall in love with it. Or at least find...

Umang Dureja

3 0
0

Recommended Articles

Meet Sandhya R, a B.Sc tutor from Bangalore

Sandhya is a proactive educationalist. She conducts classes for CBSE, PUC, ICSE, I.B. and IGCSE. Having a 6-year experience in teaching, she connects with her students and provides tutoring as per their understanding. She mentors her students personally and strives them to achieve their goals with ease. Being an enthusiastic...

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 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 >

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 Chennai
Class 10 Tuition in Mumbai
Class 10 Tuition in Pune
Class 10 Tuition in Noida
Class 10 Tuition in Lucknow
Class 10 Tuition in Gurgaon
Online Tuition Class 10

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