Question

If sin θ – cos θ = 0 then the value of (sin⁴θ + cos⁴θ) is ______.

Options

• `1/4`

• `1/2`

• `3/4`

• 1

Answer 1

If sin θ – cos θ = 0 then the value of (sin⁴θ + cos⁴θ) is `underlinebb(1/2)`.

Explanation:

(sin θ – cos θ)² = 0

⇒ (sin²θ + cos²θ) – 2 sin θ cos θ = 0

⇒ 2 sin θ cos θ = 1

⇒ `sin θ cos θ = 1/2`

∴ (sin⁴θ + cos⁴θ) = (sin²θ + cos²θ)² – 2 sin²θ cos²θ

= `(1 - 2 xx 1/4)`

= `(1 - 1/2)`

= `1/2`