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

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Answer 1 · 2018-04-16T15:30:31

$picos^(-1)x-pi^2/4$

We know that :

$cos^-1 x + sin^-1 x = pi/2$

$rArr sin^-1 x = pi/2 -cos^-1 x$ ........................... $(1)$

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

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

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

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

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