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

Prove that `sin (cot^(-1) (tan (cos^(-1) x))) = x, x gt 0`

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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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CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
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  3. Prove that sin (cot^(-1) (tan (cos^(-1) x))) = x, x gt 0

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  5. Prove that sin [2 tan^(-1) {sqrt((1 -x)/(1 + x))}] = sqrt(1 - x^(2))

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  11. Show that sin^-1 x+cos^-1 x=pi/2.

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  12. If (tan^(-1) x)^2 + (cot^(-1) x)^2 = (5 pi^2) /8 find x.

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  15. If alpha in (-(pi)/(2), 0), then find the value of tan^(-1) (cot alpha...

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