Question

If cos(α + β) = 0, then value of `cos((alpha + beta)/2)` is equal to ______.

Options

• `1/sqrt2`

• `1/2`

• 0

• `sqrt2`

Answer 1

If cos(α + β) = 0, then value of `cos((alpha + beta)/2)` is equal to `underline(1/sqrt2)`.

Explanation:

Given, 

cos (α+ β) = 0

⇒ cos (α+ β) = `cos  pi/2`

⇒ `alpha + beta = pi/2`

∴ `cos((alpha + beta)/2) = cos(pi/4) = 1/sqrt2`