Prove that \frac{\sin A}{(1+\cos A)}+\frac{(1+\cos A)}{\sin A}=2\csc A

Ramsey

Ramsey

Answered question

2021-10-30

Prove that sinA(1+cosA)+(1+cosA)sinA=2cscA

Answer & Explanation

liingliing8

liingliing8

Skilled2021-10-31Added 95 answers

We use Trigonometry identities
sinA1+cosA+1+cosAsinA=sin2A+(1+cosA)2(1+cosA)(sinA)
=sin2A+12+(cosA)2+2cosA(1+cosA)sinA
sinA1+cosA+1+cosAsinA=sin5A+1+cos5A+2cosA(1+cosA)sinA
=1+1+2cosA(1+cosA)sinA
=2+2cosA(1+cosA)(sinA)
sinA1+cosA+1+cosAsinA=2(1+csoA)(1+cosA)(sinA)=2sinA=2cscA

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?