Answer :

We need to find the value of

sin [cot-1 {tan (cos-1 x)}] …(i)

We can solve such equation by letting the inner most trigonometric function (here, cos-1 x) as some variable, and solve systematically following BODMAS rule and other trigonometric identities.

Let cos-1 x = y

We can re-write the equation (i),

sin [cot-1 {tan (cos-1 x)}] = sin [cot-1 {tan y}]

Using trigonometric identity,

[, lies in 1st Quadrant and sine, cosine, tangent and cot are positive in 1st Quadrant]

Using property of inverse trigonometry,

cot-1(cot x) = x

Using trigonometric identity,

Substituting this value of ,

We had let above that cos-1 x = y.


cos-1 x = y

x = cos y


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