The number of distinct solutions of sin5θ - cos3θ = sin9θ cos7θ in [0, π/2] is
(a) 4
(b) 5
(c) 8
(d) 9
Correct option (d) 9
Explanation:
2sin5θ cos3θ = 2sin9θ cos7θ
sin8θ + sin2θ = sin16θ + sin2θ
⇒sin16θ – sin8θ = 0
⇒2cos12θ .sin4θ = 0
∴ 9 possible values
