# Math Identities qsts, will award best answer, pls help?

prove the following:

1. (cosθ/ secθ -1) + (cosθ/ secθ +1) = 2cot^2*θ

2. (sinθ + tanθ) / (cosθ +1) = tanθ

3. (1-cos 2θ) / (sin 2θ) = tanθ

Answering even one question would be helpful, thanks so much!

### 1 Answer

Relevance

- Wayne DeguManLv 76 months agoFavorite Answer
1) [(cosθ/(secθ - 1)] + [(cosθ/(secθ + 1)] = 2cot²θ

Considering the left side we have:

cosθ/(secθ - 1) + cosθ/(secθ + 1)

so, [cosθ(secθ + 1) + cosθ(secθ - 1)]/(secθ - 1)(secθ + 1)

=> [2cosθsecθ]/(sec²θ - 1)

Now, sec²θ => tan²θ + 1 so,

[2cosθsecθ]/tan²θ

Also, secθ => 1/cosθ so,

[2cosθ/cosθ]/tan²θ

i.e. 2/tan²θ

=> 2cot²θ...RHS

:)>

Still have questions? Get your answers by asking now.