`sin^(-1)((3x)/5)+sin^(-1)((4x)/5)=sin^(-1)x` , then roots of the equation are- a.`0` b. `1` c.`-1\ ` d. `-2`

Answer

3

Explanation

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