prove that sin18 =√5_1÷4
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Step-by-step explanation:
Let θ=18. Then
5θ=90
∴2θ+3θ=90
⇒2θ=90−3θ
⇒sin2θ=sin(90−3θ)=cos3θ
⇒2sinθcosθ=4cos
3
θ−3cosθ
⇒2sinθcosθ−4cos
3
θ+3cosθ=0
⇒cosθ(2sinθ−4cos
2
θ+3)=0
⇒2sinθ−4(1−sin
2
θ)+3=0
⇒sinθ=
2×4
−2±
2
2
−4×4×(−1)
⇒sinθ=
8
−2±
20
⇒sinθ=
4
5
−1
∴sin18=
4
5
−1
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