If 4 ^ -1 x+6 ^ -1 x=3 then x= - Vidyadip

MCQ

If $4 \sin ^{-1} x+6 \cos ^{-1} x=3 \pi$ then $x=$

A
$1 / \sqrt{2}$
B
$1 / 2$
✓
0
D
$-1 / 2$

✓

Answer

Correct option: C.

0

(c) : $4 \sin ^{-1} x+6 \cos ^{-1} x=3 \pi$
$
\begin{gathered}
\Rightarrow 4 \sin ^{-1} x+6\left(\frac{\pi}{2}-\sin ^{-1} x\right)=3 \pi \\
{\left[\because \sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}\right]} \\
\Rightarrow 4 \sin ^{-1} x+3 \pi-6 \sin ^{-1} x=3 \pi \\
\Rightarrow-2 \sin ^{-1} x=0 \Rightarrow \sin ^{-1} x=0 \Rightarrow x=0
\end{gathered}
$

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