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Question
If sin 3θ = cos (θ – 6°) where 3θ and θ − 6° are acute angles, find the value of θ.
Solution
3θ, θ – 6 are an acute angle
We know that sin (90 – θ) = cos θ
sin 3θ = sin (90 – (θ - 6°))
sin 3θ = sin(90 – θ + 6°)
sin 3θ = sin (96° - θ)
3θ = 96° – θ
4θ = 96°
`θ = 96^@/4`
`θ = 24^@`
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