Question

If cos A = `1/2` then the value of sin² A + 2 cos² A is ______.

Options

• `3/2`

• `5/4`

• −1

• `1/2`

Answer 1

If cos A = `1/2` then the value of sin² A + 2 cos² A is `bbunderline(5/4)`.

Explanation:

Given: cos A = `1/2`

sin² A + 2 cos² A = (sin² A + cos² A) + cos² A

= `1 + (1/2)^2`    ...[∵ sin² A + cos² A = 1]

= `1 + 1/4`

= `(4 + 1)/4`

= `5/4`