Prove \sec\theta+\frac{1}{\tan(\theta)}=\frac{\tan(\theta)}{\sec(\theta)}

DofotheroU

DofotheroU

Answered question

2021-08-12

Prove
secθ+1tan(θ)=tan(θ)sec(θ)1

Answer & Explanation

i1ziZ

i1ziZ

Skilled2021-08-13Added 92 answers

Prove:
secθ+1tanθ=tanθsecθ1 Right hand side
tanθsecθ1=sinθcosθ(1cosθ1)=sinθ1cosθ
Razionalize the function
sinθ1cosθ×1+cosθ1+cosθ=sinθ(1+cosθ)1cos2θ
=sinθ+sinθcosθsin2θ=1sinθ+cosθsinθ
=1+cosθsinθ
Also Left hand side
secθ+1tanθ=1cosθ+1sinθcosθ=1+cosθsinθ
which is equal to right hand
Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-23Added 2605 answers

Answer is given below (on video)

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