Sin theta + sin 2 theta + sin 3 theta is equal to sin alpha and cos theta + cos 2 theta + cos 3 theta into cos alpha then theta is equals to
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Answered by
21
Answer:
θ = α/2
Step-by-step explanation:
Sinθ +Sin2θ + Sin3θ = Sinα
=> Sin3θ + Sinθ + Sin2θ = Sinα
=> 2Sin(3θ+θ/2).Cos(3θ - θ/2) + Sin2θ = Sinα
( ∵ SinA + SinB = 2Sin(A+B/2).Cos(A-B/2))
=> 2Sin2θ.Cosθ+Sin2θ = Sinα
=> Sin2θ(2 Cosθ + 1) = Sinα =============> [1]
Cosθ +Cos2θ + Cos3θ = Cosα
=> Cos3θ + Cosθ + Cos2θ = Cosα
=> 2Cos(3θ+θ/2).Cos(3θ - θ/2) + Cos2θ = Cosα
( ∵ CosA + CosB = 2Cos(A+B/2).Cos(A-B/2))
=> 2Cos2θ.Cosθ+Cos2θ = Cosα
=> Cos2θ(2 Cosθ + 1) = Cosα =============> [2]
[1] divided by [2]
Sin2θ(2 Cosθ + 1)/Cos2θ(2 Cosθ + 1) = Sinα/Cosα
Tan2θ = Tanα
2θ = α
=> θ = α/2
Answered by
3
Answer:
theta = alpha/2 so tan theta is tan(alpha/2)
Step-by-step explanation:
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