Math, asked by Tabishflash, 10 months ago

[Class 10 Trigonometry] Question is attached!

First and correct answer will be Brainliest!​

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Answers

Answered by BrainlyIAS
5

Given :

cscA+cotA=m

To Find :

\frac{m^2-1}{m^2+1}=cos\theta

Explanation :

cscA+cotA=m\\\\\implies \frac{1}{sinA}+\frac{cosA}{sinA}=m\\\\  \implies \frac{(1+cosA)}{sinA}=m\\\\ \implies m^2=\frac{(1+cosA)^2}{sin^2A} \\\\\implies m^2=\frac{cos^2A+1+2cosA}{sin^2A}\\\\

Now ,

m^2-1=\frac{cos^2A+1+2cosA}{sin^2A}-1\\\\ \implies m^2-1=\frac{cos^2A-sin^2A+2cosA+1}{sin^2A}\\\\\implies m^2-1=\frac{cos^2A-sin^2A+sin^2A+cos^2A+2cosA}{sin^2A}\\\\ \implies m^2-1=\frac{2cos^2A+2cosA}{sin^2A}...(1)

m^2+1=\frac{cos^2A+1+2cosA}{sin^2A}+1\\\\\implies m^2+1=\frac{cos^2A+sin^2A+2cosA+1}{sin^2A}\\\\ \implies m^2+1=\frac{2+2cosA}{sin^2A}...(2)

Now , do (1) / (2) , we get ,

\implies \frac{m^2-1}{m^2+1}=\frac{\frac{2cos^2A+2cosA}{sin^2A}}{\frac{2+2cosA}{sin^2A} }   \\\\\implies \frac{m^2-1}{m^2+1}=\frac{2cos^2A+2cosA}{2cosA+2}\\\\ \implies \frac{m^2-1}{m^2+1} =\frac{2cosA(cosA+1)}{2(cosA+1)} \\\\\implies \frac{m^2-1}{m^2+1}=\frac{2cosA}{2}\\\\ \implies \bold{\bf{\blue{\frac{m^2-1}{m^2+1}=cosA}}}

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