If cos(sin^-1 $\frac{2}{5}$ + cos^-1x) = 0, then x is equal to ______.

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KollegeApply · Accepted Answer

If cos(sin^-1 $\frac{2}{5}$ + cos^-1x) = 0, then x is equal to $\frac{2}{5}$. Explanation: We have, cos(sin^-1 $\frac{2}{5}$ + cos^-1x) = 0 $\Rightarrow$ `sin^-1 $\frac{2}{5}$ + cos^-1x = cos^-1 0 $\Rightarrow$ sin^-1 $\frac{2}{5}$ + cos^-1x = pi/2 $\Rightarrow$ cos^-1x = pi/2 - sin^-1 $\frac{2}{5}$ $\Rightarrow$ cos^-1x = cos^-1 $\frac{2}{5}$ .....(because cos^-1x +sin^-1x = pi/2) $\therefore$ x = $\frac{2}{5}$`

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