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  4. If the equation sin -1 x= textcosec-1 x is satisfied for α and β, (α ≠ β), then α+β is equal to

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Q. If the equation $\sin ^{-1} x=\text{cosec}^{-1} x$ is satisfied for $\alpha$ and $\beta$, $(\alpha \neq \beta)$, then $\alpha+\beta$ is equal to

Inverse Trigonometric Functions

Solution:

$\sin ^{-1} x=\sin ^{-1}\left(\frac{1}{x}\right)$
$\Rightarrow x=\frac{1}{x} \Rightarrow x^{2}=1$
$x=\pm 1$
$\alpha=1 \& \beta=-1$
hence $\alpha+\beta=0$