Question

Find the value of the following:

`tan^-1{2cos(2sin^-1  1/2)}`

Answer 1

Let `sin^-1  1/2=y`

Then,

`siny=1/2`

`thereforetan^-1{2cos(2sin^-1  1/2)}=tan^-1{2cos2y}`

`=tan^-1(2(1-2sin^2y))`     `[becausecos2x=1-2sin^2x]`

`=tan^-1{2(1-2xx1/4)}`     `[becausesiny=1/2]`

`=tan^-1{2xx1/2}`

`=tan^-1 1`

`=pi/4`

 

`thereforetan^-1{2cos(2sin^-1  1/2)}=pi/4`