Question

Proving Identities

Verify the identity$\frac{\sin \theta }{\tan \theta }=\cos \theta$

Short answer

The expression$\frac{\sin \theta }{\tan \theta }=\cos \theta$ is an identity.

Step-by-step solution

Step 1. Given information.

An expression$\frac{\sin \theta }{\tan \theta }=\cos \theta$

Step 2. Concept used.

Solve it into two part, first solve or simplify LHS. After that simplify RHS and compare both answers. If both answers are equal then it is an identity.

Step 3. Calculation.

Now, simplify LHS of $\frac{\sin \theta }{\tan \theta }=\cos \theta$:

$$\begin{gathered} \frac{\sin \theta }{\tan \theta }=\frac{\sin \theta }{\frac{\sin \theta }{\cos \theta }} \\ \frac{\sin \theta }{\tan \theta }=\cos \theta \end{gathered}$$

RHS of the equation is$\cos \theta$

Both RHS and LHS are equal. Hence it is an identity.