Chapter 20, Problem 1RE

To determine

Whether the identity “$\tan 2\theta =\frac{\cos 2\theta }{\sin 2\theta }$” is true or false.

Answer to Problem 1RE

The identity “$\tan 2\theta =\frac{\cos 2\theta }{\sin 2\theta }$”  is false.

Explanation of Solution

Formula used:

The Basic Trigonometric Identity: $\tan \theta =\frac{\sin \theta }{\cos \theta }$.

Calculation:

The given identity is $\tan 2\theta =\frac{\cos 2\theta }{\sin 2\theta }$.

By the formula stated above, $\tan 2\theta$ can be written as $\tan 2\theta =\frac{\sin 2\theta }{\cos 2\theta }$.

Hence, the identity “$\tan 2\theta =\frac{\cos 2\theta }{\sin 2\theta }$”  is false.