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Prove that sin cot^(-1) tan cos^(-1) x =...

Prove that `sin cot^(-1) tan cos^(-1) x = sin cosec^(-1) cot tan^(-1) x = x, " where " x in [0,1]`

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We have to prove that
`sin cot^(-1) tan cos^(-1) x = sin cosec^(-1) cot tan^(-1) x = x`
Now, `sin cot^(-1) tan cos^(-1) x = sin cot^(-1) tan tan.^(-1) (sqrt(1 - x^(2)))/(x)`
Also, `sin cosec^(-1) cot tan^(-1) x = sin cosec.^(-1) (1)/(x)`
`= sin (sin^(-1) x) = x`
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