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Question
If 2θ + 45° and 30° − θ are acute angles, find the degree measure of θ satisfying Sin (20 + 45°) = cos (30 - θ°)
Solution
Here 20 + 45° and 30 – θ° are acute angles:
We know that (90 – θ) = cos θ
sin (2θ + 45°) = sin (90 – (30 – θ))
sin (2θ + 45°) = sin (90 – 30 + θ)
sin (20 + 45°) = sin (60 + θ)
On equating sin of angle of we get
2θ + 45 = 60 + θ
2θ – θ = 60 – 45
θ = 15°
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