Question

If sin^-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos^-1 x is _______.

Options

• `pi/10`

• `(2pi)/5`

• `(4pi)/5`

• `(7pi)/10`

Answer 1

If sin^-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos^-1 x is `underline((2pi)/5)`.

Explanation:

Given, sin^-1 x = `pi/10`

Since, sin^-1 x + cos^-1 x = `pi/2`

`therefore pi/10 + cos^-1 x = pi/2`

∴ cos^-1 x = `pi/2 - pi/10 = (2 pi)/5`