Solve the equation frac{(2sin theta sin 2theta)}{cos theta+cos 3theta}=tan (theta) tan(2theta)

illusiia 2020-11-12 Answered
Solve the equation (2sinθsin2θ)cosθ+cos3θ=tan(θ)tan(2θ)
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Expert Answer

tafzijdeq
Answered 2020-11-13 Author has 92 answers

(2sinθsin2θ)cosθ+cos3θ
=2sin(θ)sin(2θ)2cos(θ)+4cos3(θ)
=2sin(θ)sin(2θ)2cos(θ)(1+cos2(θ))
=2sin(θ)sin(2θ)cos(θ)(2cos2(θ)1)
Use the following identity: sin(x)cos(x)=tan(x)
=sin(2θ)tan(θ)(2cos2(θ)1)
=sin(2θ)tan(θ)cos(2θ
Use the following identity: sin(x)cos(x)=tan(x)
=tan(θ)tan(2θ
Therefore
2sinθsin2θcosθ+cos3θ=tan(θ)tan(2θ)

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