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tan(pi/4+1/2cos^(-1)x)+tan(pi/4-1/2cos^(...

`tan(pi/4+1/2cos^(-1)x)+tan(pi/4-1/2cos^(-1)x),x!=0,` is equal to `x` (b) `2x` (c) `2/x` (d) none of these

A

`x`

B

`2x`

C

`(2)/(x)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`tan ((pi)/(4) + (1)/(2) cos^(-1) x) + tan ((pi)/(4) - (1)/(2) cos^(-1) x)`
`= (1 + tan ((1)/(2) cos^(-1) x))/(1 - tan((1)/(2) cos^(-1) x)) + (1- tan ((1)/(2) cos^(-1) x))/(1 + tan ((1)/(2) cos^(-1) x))`
`= ((1 + tan ((1)/(2) cos^(-1) x))^(2)+ (1- tan ((1)/(2) cos^(-1) x))^(2))/(1 - tan^(2) ((1)/(2) cos^(-1) x))`
`= 2(1 + tan^(2) ((1)/(2) cos^(-1) x))/(1 - tan^(2) ((1)/(2) cos^(-1) x))`
`= (2)/(cos(cos^(-1) x)) = (2)/(x)`
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