Practicing Success
Practicing Success
CUET Preparation Today
Value of $\frac{e^{\sin(\tan^{-1}x+\cot^{-1}x)}}{e^{\sin(\sin^{-1}x+\cos^{-1}x)}},x∈[-1,1]$, is: |
0 $\frac{π}{2}$ 1 $-\frac{π}{2}$ |
1 |
$\frac{e^{\sin(\tan^{-1}x+\cot^{-1}x)}}{e^{\sin(\sin^{-1}x+\cos^{-1}x)}}$ $=\frac{e^{\sin\frac{π}{2}}}{e^{\sin\frac{π}{2}}}=1$ $[∵\tan^{-1}x+\cot^{-1}x=\frac{π}{2}, \sin^{-1}x+\cos^{-1}x=\frac{π}{2}]$ |
