Mark the tick against the correct answer in the following:

Question:

Mark the tick against the correct answer in the following:

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

A. $\frac{3}{4}$

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

C. $\frac{3}{5}$

D. none of these

 

Solution:

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

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

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

Now, $\sin \left(\cos ^{-1} \frac{3}{5}\right)$ becomes $\sin (x)$

Since we know that $\sin x=\sqrt{1-\cos ^{2} x}$

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

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

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