Mark the tick against the correct answer in the following:

Question:

Mark the tick against the correct answer in the following:

The value of $\sin \left(\cos ^{-1} \frac{3}{5}\right)$ is

A. $\frac{2}{5}$

B. $\frac{4}{5}$

C. $\frac{-2}{5}$

D. none of these

 

Solution:

To Find: The value of $\sin \left(\cos ^{-1} \frac{3}{5}\right)$

Now, let $x=\cos ^{-1} \frac{3}{5}$

$\Rightarrow \cos x=\frac{3}{5}$

Now, $\sin x=\sqrt{1-\cos ^{2} x}$

$=\sqrt{1-\left(\frac{3}{5}\right)^{2}}$

$=\frac{4}{5}$

$\Rightarrow x=\sin ^{-1} \frac{4}{5}=\cos ^{-1} \frac{3}{5}$

Therefore,

$\sin \left(\cos ^{-1} \frac{3}{5}\right)=\sin \left(\sin ^{-1} \frac{4}{5}\right)$

Let, $Y=\sin \left(\sin ^{-1} \frac{4}{5}\right)$

$\Rightarrow \sin ^{-1} \mathrm{Y}=\sin ^{-1} \frac{4}{5}$

$\Rightarrow \mathrm{Y}=\frac{4}{5}$

 

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