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 $\sin x=\sqrt{1-\cos ^{2} x}$
$=\sqrt{1-\left(\frac{3}{5}\right)^{2}}$
$\sin \left(\cos ^{-1} \frac{3}{5}\right)=\sin x=\frac{4}{5}$