Question

`cos^-1  4/5 + tan^-1  3/5` = ______.

Options

• `tan^-1  27/11`

• `sin^-1  11/27`

• `cos^-1  11/27`

• `cot^-1  27/11`

Answer 1

`cos^-1  4/5 + tan^-1  3/5` = `tan^-1  27/11`.

Explanation:

Let α = `cos^-1  (4/5)`

∴ cos α = `(4/5)

⇒ tan α = `(3/4)`

∴ α =  `tan^-1 (3/4)`

∴ `cos^-1  4/5 + tan^-1  3/5`

= `tan^-1  3/4 + tan^-1  3/5`

= `tan^-1 ((3/4 + 3/5)/(1 - 3/4*3/5))`

= `tan^-1 (27/11)`