((cos^-1 (x))^2) - (sin^-1 (x)^2) = ?

1 Answer
Kalit Gautam
Apr 16, 2018

picos^(-1)x-pi^2/4πcos−1x−π24

Explanation:

We know that :

cos^-1 x + sin^-1 x = pi/2cos−1x+sin−1x=π2

rArr sin^-1 x = pi/2 -cos^-1 x ⇒sin−1x=π2−cos−1x...........................(1)(1)

Put the value of (1)(1) in the question , we get :-

(cos^-1 x)^2 - (sin^-1 x)^2 = (cos^-1 x)^2 - (pi/2 -cos^-1 x )^2(cos−1x)2−(sin−1x)2=(cos−1x)2−(π2−cos−1x)2

= (cos^-1 x)^2 -pi^2/4-(cos^-1 x)^2+picos^-1 x=(cos−1x)2−π24−(cos−1x)2+πcos−1x

=cancel ((cos^-1 x)^2) -pi^2/4-cancel((cos^-1 x)^2)+picos^-1 x

=picos^-1 x-pi^2/4

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