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if y=sin^-1[sqrt(x-ax)-sqrt(a-ax)] then ...

if `y=sin^-1[sqrt(x-ax)-sqrt(a-ax)]` then prove that `1/(2sqrtx sqrt(1-x))`

A

`(1)/ (sinsqrt(a - ax))`

B

` sin sqrt(x)* sin sqrt(x)`

C

`(1)/ (2sqrt(x)sqrt(1-x))`

D

zero

Text Solution

Verified by Experts

The correct Answer is:
C
Put ` x = sin^(2) theta " and " a = sin^(2) phi `, then
` y = sin^(-1) (sin theta cos phi - cos theta sin phi)`
` = sin^(-1)[ sin ( theta - phi)] = theta - phi `
`= sin^(-1) sqrt(x)- sin^(-1) sqrt(a) `
` therefore (dy)/(dx) = (1)/(sqrt( 1 - x)).(1)/(2 sqrt(x))`
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