If sin 5θ + sin θ = sin 3θ and 0 < θ < (π/2), then what is the value of θ (in degrees)?
Expression : $$sin5\theta+sin\theta=sin3\theta$$
Using, $$sinC+sinD = 2sin(\frac{C+D}{2})cos(\frac{C-D}{2})$$
=> $$2sin(\frac{5\theta+\theta}{2})cos(\frac{5\theta-\theta}{2})=sin3\theta$$
=> $$2sin3\theta cos2\theta=sin3\theta$$
=> $$cos2\theta=\frac{1}{2}$$
=> $$2\theta=cos^{-1}(\frac{1}{2})$$
=> $$2\theta=60^\circ$$
=> $$\theta=\frac{60}{2}=30^\circ$$
=> Ans - (A)
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