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The value of cos^(-1)sqrt(2/3)-cos^(-1)(...

The value of `cos^(-1)sqrt(2/3)-cos^(-1)(sqrt(6)+1)/(2sqrt(3))` is equal to `pi/3` (b) `pi/4` (c) `pi/2` (d) `pi/6`

A

`(pi)/(3)`

B

`(pi)/(4)`

C

`(pi)/(2)`

D

`(pi)/(6)`

Text Solution

Verified by Experts

The correct Answer is:
D
`cos^(-1) (sqrt((2)/(3))) - cos^(-1) ((sqrt6 + 1)/(2sqrt3))`
`= tan^(-1) ((1)/(sqrt2)) - tan^(-1) ((sqrt3 -sqrt2)/(1 + sqrt6))`
`= tan^(-1)((1)/(sqrt2)) -[tan^(-1) sqrt3 - tan^(-1) sqrt2]`
`= (tan^(-1).(1)/(sqrt2) + tan^(-1) sqrt2) - tan^(-1) sqrt3`
`= (pi)/(2) - (pi)/(3) = (pi)/(6)`
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