The value of `sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))),`where `x in (pi/2,pi)`, is equal to`pi/2`(b) `-pi`(c) `pi`(d) `-pi/2`A. `(pi)/(2)`B. `-pi`C. `pi`D. `-(pi)/(2)`

The value of `sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))),`where `x

1.	The value of `sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))),`where `x in (pi/2,pi)`, is equal to`pi/2`(b) `-pi`(c) `pi`(d) `-pi/2`A. `(pi)/(2)`B. `-pi`C. `pi`D. `-(pi)/(2)`
Answer» Correct Answer - D `sin^(-1) (cos (cos^(-1) (cos x) + sin^(-1) (sin x)))` `= sin^(-1) (cos (x + pi - x)) " " ["as " x in (pi//2)]` `= sin^(-1) (cos pi) = sin^(-1) (-1) = -(pi)/(2)`

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