Question

True or False. $\sin \left(2\theta \right)$has two equivalent forms:

$2\sin u\cos u$and ${\sin }^2\theta -{\cos }^2\theta$

Short answer

The given statement is false.

Step-by-step solution

Step 1. Given information

Two equivalent forms of $\sin 2\theta$are given i.e., $2\cos \theta \sin \theta$and${\sin }^2\theta -{\cos }^2\theta$

Step 2. True or False

From double angle formula, we know that:

$\sin 2\theta =2\sin \theta \cos \theta$but

$\sin 2\theta \ne {\sin }^2\theta -{\cos }^2\theta$

So, this statement is false.