Question

sinθ + sin 3θ + sin 5θ = 0.​

Answer 1

Answer:

sin θ + sin 3θ + sin 5θ = 0

or, (sin θ + sin 5θ) + sin 3θ = 0

or, 2 sin 3θ cos 2θ + sin 3θ = 0

or, sin 3θ (2 cos 2θ + 1) = 0

or, sin 3θ = 0

or cos 2θ = –1/2 When sin 3θ = 0

, then 3θ = nπ or θ =nπ/3

When cos 2θ = –1/2 = cos2π/3,  then 2θ = 2nπ ± 2π/3 or, θ = nπ ± π/3

which gives

All these values of θ are contained in θ = nπ/3, n ∈ Z.

Hence, the required solution set is given by {θ : θ = nπ/3, n ∈ Z}

Step-by-step explanation:

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