Prove sin(Θ)tan(Θ) = cos(Θ)sec²(Θ) - cos(Θ)

[snowpanda]

Homework Statement

Prove (using the left side):

sinΘ tanΘ = cosΘ sec^2Θ - cosΘ

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

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

Now use the fact that $tan^2(\theta)= sec^2(\theta)- 1$.