How do you prove that tan^2 θ•cos^2 θ + cos^2 θ = 1?

Question

anonymous · Answer

$$\tan^2\theta=\frac{\sin^2\theta}{\cos^2\theta}$$

anonymous · Answer

Where do I go from there?

anonymous · Answer

substitute it in the equation

anonymous · Answer

$$\tan^2\theta\cos^2\theta=\frac{\sin^2\theta}{\cos^2\theta}\times\cos^2\theta=\cdots$$
So you have on the left side
$$\cdots+\cos^2\theta$$

anonymous · Answer

So (sin2 θ/cos2 θ)•cos2 θ + cos2 θ = 1

anonymous · Answer

yeah

anonymous · Answer

How do I simplify it to equal 1? I have to show my work or my teacher won't grade it

anonymous · Answer

I think I got it. Don't answer as yet @ranga, I might need you soon

ranga · Answer

I will use x instead of theta as it is easier to type.
tan^2 x•cos^2 x + cos^2 x =
sin^2(x) / cos^2(x) * cos^2(x) + cos^2(x) =
sin^2(x) + cos^2(x)
There is a trigonometric identity that says: sin^2(x) + cos^2(x) = 1

anonymous · Answer

Ok well I guess I didn't have it lol. My answer looked like sin2 θ/cos2 θ=1

anonymous · Answer

Thank you once more @ranga. You're awesome

ranga · Answer

You are welcome.