How do you prove that $sin(cot^(-1)(tan(cos^(-1)(sin x))))=sin x$ ?

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Answer 1 · 2016-11-04T03:02:31

$LHS=sin(cot^(-1)(tan(cos^(-1)(sin x))))$

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

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

$=sin(cot^(-1)(cot(x)))$

$=sinx=RHS$

Proved

How do you prove that sin(cot^(-1)(tan(cos^(-1)(sin x))))=sin xsin(cot^(-1)(tan(cos^(-1)(sin x))))=sin x?