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Let tan^(-1) y = tan^(-1) x + tan^(-1) (...

Let `tan^(-1) y = tan^(-1) x + tan^(-1) ((2x)/(1 -x^(2))), " where " |x| lt (1)/(sqrt3)`. Then a value of y is

A

`(3x-x^(3))/(1+3x^(2))`

B

`(3x+x^(2))/(1+3x^(2))`

C

`(3x-x^(3))/(1-3x^(2))`

D

`(3x+x^(3))/(1-3x^(2))`

Text Solution

Verified by Experts

We have
`tan^(-1)y=tan^(-1)x+tan^(-1)(2x)/(1-x^(2))` ltMbrgt `rarr tan^(-1)y=tan^(-1)x+2 tan^(-1)x=3 tan^(-1)x=tan^(-1)(3x-x^(3))/(1-3x^(22))`
`rarr y=(3x-x^(3))/(1-3x^(2))`
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OBJECTIVE RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
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