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The equation sin^-1x-cos^-1x=cos^-1(sqrt...

The equation `sin^-1x-cos^-1x=cos^-1(sqrt3/2)` has

A

No solution

B

Unique solution

C

Infinite solution

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`"sin"^(-1)x-"cos"^(-1) x="cos"^(-1)((sqrt(3))/(2))`
`rArr (pi)/(2) -"cos"^(-1)x-"cos"^(-1)x="cos"^(-1)((sqrt(3))/(2))`
`rArr (pi)/(2)-(pi)/(6) =2 "cos"^(-1) x`
`rArr"cos"^(-1) x=(pi)/(6)`
`rArrx=(sqrt(3))/(2)`
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