If sin θ + cos θ = 5/4 and θ is an acute angle, what is the value of sin⁴ θ + cos⁴ θ?
Show answer & explanation
Correct answer: B
Explanation
Given,
sin θ + cos θ = 5/4
On squaring both sides,
(sin θ + cos θ)² = 25/16
1 + 2sin θ cos θ = 25/16
2sin θ cos θ = 9/16
sin θ cos θ = 9/32
sin⁴ θ + cos⁴ θ = (sin² θ + cos² θ)² − 2sin² θ cos² θ
= 1 − 2(9/32)²
= 1 − 2 × 81/1024
= 1 − 81/512
= 431/512