Solve the equation frac{1}{csc theta-cos theta}=frac{1+cos theta}{sin theta}

CMIIh 2020-11-23 Answered
Solve the equation 1cscθcosθ=1+cosθsinθ
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Expert Answer

gotovub
Answered 2020-11-24 Author has 98 answers

We work using the left side. Write in terms of sine and cosine:
1cscθcosθ=11sinθcosθsinθ
1cscθcosθ=11cosθsinθ
1cscθcosθ=sinθ1cosθ
Multiply by 1+cosθ1+cosθ:
1cscθcosθ=sin1cosθ×1+cosθ1+cosθ
1cscθcosθ=sinθ(1+cosθ)1cos2θ
Use the Pythagorean identity: sin2θ+cos2θ=1 and sin2θ=1cos2θ
1cscθcosθ=sinθ(1+cosθ)sin2θ
1cscθcosθ=1+cosθsinθ

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