Question

y=sin⁻¹ 2x√1-x², 1/√2

Answer 1

Answer:

y = 90°

Step-by-step explanation:

As given in the question $y = sin^{-1}2x\sqrt{1-x^{2}}$

we have to find the value of y at $x= \frac{1}{\sqrt{2} }$

Now, substitute the value of x in the equation $y = sin^{-1}2x\sqrt{1-x^{2}}$

    $\Rightarrow y = sin^{-1}2x\sqrt{1-x^{2}}$

    $\Rightarrow y = sin^{-1}2\left ( \frac{1}{\sqrt{2}} \right )\sqrt{1-\left ( \frac{1}{\sqrt{2}} \right )^{2}}$

    $\Rightarrow y = sin^{-1}\left ( 2\times \frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}} \right )$

    $\Rightarrow y = sin^{-1}\left ( \frac{2}{2} \right )$

    $\Rightarrow y = sin^{-1}\left ( 1 \right )$

    $\Rightarrow y =90-degree$

Hence , the value of y = 90° .