If 1 + sin ⁡ θ + sin 2 ⁡ θ + sin 3 ⁡ θ + . . . ∞ = 4 + 2 3 , 0 θ π , then

Question

If 1 + sin ⁡ θ + sin 2 ⁡ θ + sin 3 ⁡ θ + . . . ∞ = 4 + 2 3 , 0 θ π , then, θ = π 3, θ = π 6, θ = π 3 or π 6, θ = π 3 or 2 π 3

MARKS App · Accepted Answer

Given, 1 + sin ⁡ θ + sin 2 ⁡ θ + sin 3 ⁡ θ + … ∞ = 4 + 2 3 ⇒ 1 1 - sin ⁡ θ = 4 + 2 3 [ ∵ 0 sin ⁡ θ 1 ] ⇒ 1 - sin ⁡ θ = 4 - 2 3 16 - 12 = 1 - 3 2 ⇒ sin ⁡ θ = 3 2 ⇒ θ = π 3 or 2 π 3

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