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if cot 4θ+cot2θ=1 prove that sin4θ+ sin2θ =1
Asked by bimanmandal53361 | 15 Jan, 2024, 12:32: AM

cot4θ + cot2θ = 1

In above expression , numerator is simplified as cos(4θ - 2 θ )

Hence we get,   cos(4θ - 2 θ ) = sin4θ sin2θ

cos2θ  = sin4θ sin2θ = 2 sin2θ cos2θ sin2θ

Dividing both sides by cos2θ, we get

1  = 2 sin22θ

1 - 2 sin22θ = cos(4θ) = 0

4θ = π/2   or  θ = π/8

sin4θ + sin2θ = sin(π/2 ) + sin(π/4) = 1 + ( 1/√2 )

( Value for the expression " sin4θ + sin2θ " is as above not 1 . I checked using EXCEL . Above value is correct )

Answered by Thiyagarajan K | 15 Jan, 2024, 08:32: AM

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