Prove: \(\displaystyle{\frac{{{1}-{\cos{{2}}}\theta}}{{{1}-{\cos{\theta}}}}}={2}{\cos{\theta}}-{2}\)

Jazmyn Holden

Jazmyn Holden

Answered question

2022-03-31

Prove:
1cos2θ1cosθ=2cosθ2

Answer & Explanation

Drahthaare89c

Drahthaare89c

Beginner2022-04-01Added 19 answers

We have, using cos2θ=2cos2θ1
1(2cos2θ1)1cosθ=2(1cos2θ)1cosθ
=2(1cosθ)(1+cosθ)1cosθ
=2(1+cosθ)
Since 1cos2θ is a difference of two squares. The result you asked for in your question is wrong. This is the correct result. So, we have
1cos22θ1cosθ=2cosθ+2
As you can see, the above is equivalent to
1cos22θ1cosθ2cosθ=2
So the same proof works!

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