Question

If sinA + sin²A = 1, then the value of the expression (cos²A + cos⁴A) is ______.

Options

• 1

• `1/2`

• 2

• 3

Answer 1

If sinA + sin²A = 1, then the value of the expression (cos²A + cos⁴A) is 1.

Explanation:

Given,

sinA + sin²A = 1

⇒ sinA = 1 – sin²A = cos²A   ...[∵ sin²θ + cos²θ = 1]

On squaring both sides, we get

sin²A = cos⁴A

⇒ 1 – cos²A = cos⁴A

⇒ cos²A + cos⁴A = 1