Question

If `cos(sin^-1  2/5 + cos^-1x)` = 0, then x is equal to ______.

Options

• `1/5`

• `2/5`

• 0

• 1

Answer 1

If `cos(sin^-1  2/5 + cos^-1x)` = 0, then x is equal to `2/5`.

Explanation:

We have, `cos(sin^-1  2/5 + cos^-1x)` = 0

⇒ `sin^-1  2/5 + cos^-1x = cos^-1 0`

⇒ `sin^-1  2/5 + cos^-1x = pi/2`

⇒ `cos^-1x = pi/2 - sin^-1  2/5`

⇒ `cos^-1x = cos^-1  2/5`   .....`(because cos^-1x +sin^-1x = pi/2)`

∴ x = `2/5`