Answer:
[tex]2cos^2(\theta) - 1 = cos(2\theta)[/tex]
Explanation:
Given
[tex]2cos^2(\theta) - 1[/tex]
Required
Simplify
In trigonometry:
[tex]sin^2(\theta) + cos^2(\theta) = 1[/tex]
So; the given expression becomes
[tex]2cos^2(\theta) - (sin^2(\theta) + cos^2(\theta))[/tex]
Open Bracket
[tex]2cos^2(\theta) - sin^2(\theta) - cos^2(\theta)[/tex]
Collect Like Terms
[tex]2cos^2(\theta) - cos^2(\theta)- sin^2(\theta)[/tex]
[tex]cos^2(\theta)- sin^2(\theta)[/tex]
In trigonometry:
[tex]cos(\theta + \theta) = cos^2(\theta)- sin^2(\theta)[/tex]
This implies that:
[tex]cos^2(\theta)- sin^2(\theta) = cos(\theta + \theta)[/tex]
=
[tex]cos(\theta + \theta)[/tex]
[tex]cos(2\theta)[/tex]
Hence:
[tex]2cos^2(\theta) - 1 = cos(2\theta)[/tex]
