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

the value of `cos^-1sqrt(2/3)-cos^-1 ((sqrt6+1)/(2sqrt3))` is equal to:

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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CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise (Single)
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  10. If cot^(-1)x+cot^(-1)y+cot^(-1)z=pi/2,x , y , z >0a n dx y<1, then x+y...

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  19. The value 2tan^(-1)[sqrt((a-b)/(a+b)tantheta/2)] is equal to cos^(-1)(...

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