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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