if

Question:

If $\frac{\sin ^{-1} x}{a}=\frac{\cos ^{-1} x}{b}=\frac{\tan ^{-1} y}{c} ; 0

  1. (1) $\frac{1-y^{2}}{2 y}$

  2. (2) $\frac{1-y^{2}}{1+y^{2}}$

  3. (3) $1-y^{2}$

  4. (4) $\frac{1-y^{2}}{y \sqrt{y}}$


Correct Option: , 2

Solution:

$\frac{\sin ^{-1} x}{a}=\frac{\cos ^{-1} x}{b}=\frac{\tan ^{-1} y}{c}$

$\frac{\sin ^{-1} x}{a}=\frac{\cos ^{-1} x}{b}=\frac{\sin ^{-1} x+\cos ^{-1} x}{a+b}=\frac{\pi}{2(a+b)}$

Now, $\frac{\tan ^{-1} y}{c}=\frac{\pi}{2(a+b)}$

$2 \tan ^{-1} y=\frac{\pi c}{a+b}$

$\Rightarrow \quad \cos \left(\frac{\pi c}{a+b}\right)=\cos \left(2 \tan ^{-1} y\right)=\frac{1-y^{2}}{1+y^{2}}$

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now