Question

Prove: tan2 θ•cos2 θ + cos2 θ = 1. You must show all work.

Answer 1

Is it :

\[\tan^2(\theta) \cos^2(\theta) + \cos^2(\theta) = 1 \; \; ??\]

Answer 2

Then you must know that:

\[\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \implies \tan^2(\theta) = \frac{\sin^2(\theta)}{\cos^2(\theta)}\]

Just put it in place of \(tan^2(\theta)\) there and you will get what you want.. :)

Answer 3

re-write tan²θ in terms of sines and cosines, and cancel the cos²θ .

Answer 4

and then sin²θ+cos²θ=1 is an identity (we can prove it too, if you want)