CBSE Class 11-science Answered
if cot 4θ+cot2θ=1 prove that sin4θ+ sin2θ =1
Asked by bimanmandal53361 | 15 Jan, 2024, 12:32: AM
Expert Answer
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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