Q106 / 160 · TS EAMCET 2023 (14 May Shift 1) · Mathematics

If $\sin y=\sin 3 t$ and $x=\sin t$, then $\frac{d y}{d x}=$

  • A
    $\frac{3}{\sqrt{4-x^2}}$
  • Correct answer
    B
    $\frac{3}{\sqrt{1-x^2}}$
  • C
    $\frac{1}{\sqrt{4-x^2}}$
  • D
    $\frac{-1}{\sqrt{4-x^2}}$

Solution

$\sin y=\sin 3 t$ $\begin{aligned} & t=3 t \\ & y=3 \sin ^{-1} x \\ & \frac{d y}{d x}=\frac{d}{d x} 3 \sin ^{-1} x \\ & =\frac{3}{\sqrt{1-x^2}}\end{aligned}$

Hence, the correct answer is option: 'B'.

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