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Question

Find all the values of θ satisfying the equation : sinθ+sin5θ=sin3θ such that 0θπ.

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Solution

sinθ+sin5θ=sin3θsinθsin3θ+sin5θ=03sinθ16sin3θ+16sin5θ=0sinθ(2sinθ1)(1+2sinθ)(4sin2θ3)=0
sinθ=0 or sinθ=12 or sinθ=12 or sinθ=±32
For 0θπ
We get θ=0,π6,π3,2π3,5π6,π

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