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If f(x)=sin^(-1)((sqrt(3))/2x-1/2sqrt(1-...

If `f(x)=sin^(-1)((sqrt(3))/2x-1/2sqrt(1-x^2)),-1/2lt=xlt=1,t h e nf(x)` is equal to

A

`sin^(-1)(1)/(2)-sin^(-1)x`

B

sin^(-1)x-(pi)/(6)`

C

`sin^(-1)x+(pi)/(6)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Put `x=sintheta`, we get
`f(x)=sin^(-1){sin(theta-(pi)/(6))}`
For `-(1)/(2)lexle1rArr-(1)/(2)lesinthetale1`
`rArr-(pi)/(6)lethetale(pi)/(2)`
`thereforef(x)=theta-(pi)/(6)=sin^(-1)x-(pi)/(6)`
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