- #1

- 5

- 4

- Homework Statement
- Morning, I hope someone could help me. I've tackled this one a few times and keep getting stuck.

Essentially its to establish the following identity

- Relevant Equations
- $$\frac{\sin \theta + \tan \theta}{\csc \theta + \cot \theta} = \sin \theta \tan \theta$$

My latest attempt

\begin{align*}

\frac{\sin \theta + \tan \theta}{\csc \theta + \cot \theta} = \\

\frac{\sin \theta + \tan \theta}{\csc \theta + \cot \theta} \cdot \frac{\csc \theta - \cot \theta}{\csc \theta - \cot \theta} =\\

\frac{\sin \theta \csc \theta + \tan\theta \csc \theta - \sin \theta \cot \theta - \tan \theta \cot \theta}{\csc^2 \theta - \cot^2 \theta} = \\

\frac{1 + \tan\theta \csc \theta - \sin \theta \cot \theta - 1}{\csc^2 \theta - \cot^2 \theta} = \\

\frac{\tan\theta \csc \theta - \sin \theta \cot \theta }{\csc^2 \theta - \cot^2 \theta} = \\

\frac{\tan\theta \csc \theta - \sin \theta \cot \theta }{1} = \\

\frac{\tan\theta}{\sin \theta} - \frac{\sin \theta} {\tan \theta} = \\

\end{align*}

I would even be grateful for any resources on solving problems like this, I have checked out few youtube videos which are helping, but the problems explained tend to have less terms.

Many thanks in advance

\begin{align*}

\frac{\sin \theta + \tan \theta}{\csc \theta + \cot \theta} = \\

\frac{\sin \theta + \tan \theta}{\csc \theta + \cot \theta} \cdot \frac{\csc \theta - \cot \theta}{\csc \theta - \cot \theta} =\\

\frac{\sin \theta \csc \theta + \tan\theta \csc \theta - \sin \theta \cot \theta - \tan \theta \cot \theta}{\csc^2 \theta - \cot^2 \theta} = \\

\frac{1 + \tan\theta \csc \theta - \sin \theta \cot \theta - 1}{\csc^2 \theta - \cot^2 \theta} = \\

\frac{\tan\theta \csc \theta - \sin \theta \cot \theta }{\csc^2 \theta - \cot^2 \theta} = \\

\frac{\tan\theta \csc \theta - \sin \theta \cot \theta }{1} = \\

\frac{\tan\theta}{\sin \theta} - \frac{\sin \theta} {\tan \theta} = \\

\end{align*}

I would even be grateful for any resources on solving problems like this, I have checked out few youtube videos which are helping, but the problems explained tend to have less terms.

Many thanks in advance