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The number of distinct solutions of sin5θ - cos3θ = sin9θ cos7θ in [0, π/2] is

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The number of distinct solutions of sin5θ -  cos3θ = sin9θ cos7θ  in [0, π/2] is

(a)  4

(b)  5

(c)  8

(d)  9 

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1 Answer

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Best answer

Correct option  (d) 9

Explanation:

2sin5θ cos3θ = 2sin9θ cos7θ

sin8θ + sin2θ = sin16θ + sin2θ

⇒ sin16θ – sin8θ = 0

⇒ 2cos12θ .sin4θ = 0

∴ 9 possible values

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