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For the principal values, evaluate ea...

For the principal values, evaluate each of the following : `sin^(-1)(-1/2)+2cos^(-1)(-(sqrt(3))/2)` (ii) `sin^(-1)(-(sqrt(3))/2)+cos^(-1)((sqrt(3))/2)`

A

`1/sqrt(26)`

B

`5/sqrt(26)`

C

`1/sqrt(24)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Range of `cos^(-1)` is `[0,pi]`.
`cos^(-1)(-sqrt(3)/2)=x rArr cosx=-sqrt(3)/2 =-cospi/6 = cos(pi-pi/6)=cos(5p)/6 rArr x=(5pi)6`
`sin^(-1)(-1/2)+2cos^(-1)(-sqrt(3)/2)=-sin^(-1)1/2+2 xx (5pi)/6 = -pi/6+(5pi)/6=(9pi)/6=(3pi)/2`.
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