If f θ = cos 2 ⁡ θ cos ⁡ θ sin ⁡ θ - sin ⁡ θ cos ⁡ θ sin ⁡ θ sin 2 ⁡ θ cos ⁡ θ sin ⁡ θ - cos ⁡ θ 0 then, f π 6 + f π 3 + f π 2 + f 2 π 3 + f 5 π 6 + f π + . … … . + f 53 π 6 is equal to

Question

If f θ = cos 2 ⁡ θ cos ⁡ θ sin ⁡ θ - sin ⁡ θ cos ⁡ θ sin ⁡ θ sin 2 ⁡ θ cos ⁡ θ sin ⁡ θ - cos ⁡ θ 0 then, f π 6 + f π 3 + f π 2 + f 2 π 3 + f 5 π 6 + f π + . … … . + f 53 π 6 is equal to,

MARKS App · Accepted Answer

f θ = cos 2 ⁡ θ cos 2 ⁡ θ - cos ⁡ θ sin ⁡ θ - cos ⁡ θ sin ⁡ θ - sin ⁡ θ - cos 2 ⁡ θ sin ⁡ θ - sin 3 ⁡ θ = cos 4 ⁡ θ + sin 4 ⁡ θ + 2 cos 2 ⁡ θ sin 2 ⁡ θ = cos 2 ⁡ θ + sin 2 ⁡ θ 2 = 1 f π 6 = f 2 π 6 = f 3 π 6 = . … … . = f 53 π 6 = 1

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