Question

Simplify cos^2 theta(1 + tan^2 theta)

Answers:
cos^2 theta + sin^2 theta
cos^2 theta
1
-1

Answer 1

By definition of tangent,

`\tan\theta=(\sin\theta)/(\cos\theta)\implies\tan^2\theta=(\sin^2\theta)/(\cos^2\theta)`

Distribute the squared cosine:

`\cos^2\theta\left(1+(\sin^2\theta)/(\cos^2\theta)\right)=\cos^2\theta+\sin^2\theta=1`

where the last step is simply applying the Pythagorean identity.