Question

The value of `tan(cos^-1  4/5 + tan^-1  2/3)` is ______.

Options

• `6/17`

• `7/16`

• `17/6`

• `16/7`

Answer 1

The value of `tan(cos^-1  4/5 + tan^-1  2/3)` is `underlinebb(17/6)`.

Explanation:

`tan(cos^-1  4/5 + tan^-1  2/3)`

Let `cos^-1  4/5` = θ,

∴ cos θ = `4/5`

∴ tan θ = `3/4`, 

∴ θ = `tan^-1  3/4`

i.e. `cos^-1  4/5 = tan^-1  3/4`

∴ Given expression becomes

= `tan(tan^-1  3/4 + tan^-1  2/3)`

= `tan[tan^-1 ((3/4 + 2/3)/(1 - 6/12))]`

= `tan[tan^-1  17/6]`

= `17/6`