We have to prove that arc sin x + arc cos x = pi/2
The left hand side is
arc sin x + arc cos x
take the sine of the angle
sin (arc sin x + arc cos x)
=> sin (arc sin x)* cos (arc cos x) + cos (arc sin x)* sin (arc cos x)
use the relation sin (arc cos x) = cos (arc sin x) = sqrt (1 - x^2)
=> x*x + [sqrt (1 - x^2)]^2
=> x^2 + 1 - x^2
=> 1
Take the sine of the right hand side
sin pi/2 = 1
We get the same value in both the cases
This proves that arc sin x + arc cos x = pi/2
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