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1.

If sin 3θ = cos (θ – 6°), where 3θ and θ – 6° are acute angles, find the value of θ.

Answer»

sin 3θ = cos (θ – 6°)

⇒ cos (90° – 3θ) = cos (θ – 6°)

⇒ 90° – 3θ = θ – 6° ⇒ 4θ = 96° ⇒ θ = 24°.