Mathematics

# Solve:- ${\sin ^{ - 1}}(\cos x)$

##### SOLUTION
$\sin^{-1}\left ( \cos x \right )= x+\frac{\Pi}{2}$
Explanation:
We know that the cosine function, is nothing more than the $sine \frac{\Pi }{2}$ radians out of phase, as proved below:
$cos(θ−\frac{\Pi }{2}) = cos(θ)cos(−\frac{\Pi }{2})−sin(θ)sin(−\frac{\Pi }{2})$
$cos(θ−\frac{\Pi }{2}) = cos(θ). 0 −\left (-sin(θ)sin(\frac{\Pi }{2})\right )$
$cos(θ−\frac{\Pi }{2}) = \sin(θ)$
So we can say that the sine function, 90 degrees ahead, is the cosine function.
Using the property of inverse functions that \displaystyle $f^{-1}\left ( f\left ( x \right ) \right )=x$
$\sin^{-1}\left ( \cos x \right )= x+\frac{\Pi}{2}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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