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  4. If x=(1/5) the value of cos((cos)- 1 x + 2 (sin)- 1 x) is

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Q. If $x=\frac{1}{5}$ the value of $cos\left(\left(cos\right)^{- 1} x + 2 \left(sin\right)^{- 1} x\right)$ is

NTA AbhyasNTA Abhyas 2022

Solution:

The given expression is equal to
$cos\left(\left(cos\right)^{- 1} x + \left(sin\right)^{- 1} x + \left(sin\right)^{- 1} x\right)$
$=cos\left(\frac{\pi }{2} + \left(sin\right)^{- 1} x\right)=-sin\left(\left(sin\right)^{- 1} x\right)=-x=-\frac{1}{5}$
$\left[Using cos^{- 1} x + sin^{- 1} x = \frac{\pi }{2}\right]$