Question

Enter the expression 2cos2(θ)−1 , where θ is the lowercase Greek letter theta.

Answer 1

Answer:

$2cos^2(\theta) - 1 = cos(2\theta)$

Explanation:

Given

$2cos^2(\theta) - 1$

Required

Simplify

In trigonometry:

$sin^2(\theta) + cos^2(\theta) = 1$

So; the given expression becomes

$2cos^2(\theta) - (sin^2(\theta) + cos^2(\theta))$

Open Bracket

$2cos^2(\theta) - sin^2(\theta) - cos^2(\theta)$

Collect Like Terms

$2cos^2(\theta) - cos^2(\theta)- sin^2(\theta)$

$cos^2(\theta)- sin^2(\theta)$

In trigonometry:

$cos(\theta + \theta) = cos^2(\theta)- sin^2(\theta)$

This implies that:

$cos^2(\theta)- sin^2(\theta) = cos(\theta + \theta)$

=

$cos(\theta + \theta)$

$cos(2\theta)$

Hence:

$2cos^2(\theta) - 1 = cos(2\theta)$