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If alpha=sin^(-1)(cos(sin^(-1)x))a n dbe...

If `alpha=sin^(-1)(cos(sin^(-1)x))a n dbeta=cos^(-1)("sin"(cos^(-1)x)),` then find `tanalphadottanbeta`

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`beta = cos^(-1) (sin ((pi)/(2) - sin^(-1) x))`
`= cos^(-1) [cos (sin^(-1) x)]`
Also, `alpha = sin^(-1) [cos (sin^(-1) x)]`
`:. alpha + beta = (pi)/(2)`
`rArr tan alpha = cot beta " or " tan alpha. tan beta = 1`
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