It's trigo time #11 (new)

Geometry Level 2

Simplify the following:

sin ⁡ 2 θ 1 − cos ⁡ 2 θ \large \frac{\sin\ 2\theta }{1-\cos 2 \theta }

Prove your answer.

This is a part of the set: It's trigo time

cot ⁡ θ \cot\theta cos ⁡ θ \cos\theta sin ⁡ 2 θ \sin^2\theta sec ⁡ θ \sec\theta

Syed Hamza Khalid by Syed Hamza Khalid , 17, France

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Chew-Seong Cheong
May 19, 2017

sin ⁡ 2 θ 1 − cos ⁡ 2 θ = 2 sin ⁡ θ cos ⁡ θ 1 − ( 1 − 2 sin ⁡ 2 θ ) = 2 sin ⁡ θ cos ⁡ θ 2 sin ⁡ 2 θ = cos ⁡ θ sin ⁡ θ = cot ⁡ θ \begin{aligned} \frac {\sin 2\theta}{1-\cos 2 \theta} & = \frac {2\sin \theta \cos \theta}{1-(1-2\sin^2 \theta)} \\ & = \frac {2\sin \theta \cos \theta}{2\sin^2 \theta} \\ & = \frac {\cos \theta}{\sin \theta} \\ & = \boxed{\cot \theta} \end{aligned}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...