Let `tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^2))`, where `|x|

1.	Let `tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^2))`, where `\|x\|
Answer» Correct Answer - B `(-1)/(sqrt3) lt x lt (1)/(sqrt3)` Let `x = tan theta` `:. (-pi)/(6) lt theta lt (pi)/(6)` `:. Tan^(-1) y = theta + tan^(-1) tan 2 theta = theta + 2theta = 3 theta` `:. Y = tan 3 theta = (3 tan theta - tan^(3) theta)/(1-3 tan^(2) theta)` `:. y = (3x -x^(3))/(1 -3x^(2))`

Discussion

`tan^(-1)[(cosx)/(1+sinx)]`is equal to`pi/4-x/2,forx in (-pi/2,(3pi)/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-(3pi)/2,pi/2)`
The value of `sin^(-1)(sin12)+sin^(-1)(cos12)=`
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