Question

If sin θ – cos θ = 0, then find the value of sin⁴ θ + cos⁴ θ.

Answer 1

sin θ – cos θ = 0

sin θ = cos θ

`sinθ/cosθ` = 1

`\implies` tan θ = tan 45°

∴ θ = 45°

Now sin⁴ θ + cos⁴ θ = sin⁴ 45° + cos⁴ 45°

= `(1/sqrt(2))^4 + (1/sqrt(2))^4`

= `1/4 + 1/4`

= `2/4`

sin⁴ θ + cos⁴ θ = `1/2`