Question

Write the trigonometric expression in terms of sine and cosine, and then simplify.
tan θ/ sec θ − cos θ

Answer 1

tan(θ)=sin(θ) / cos(θ) and sec(θ) = 1/cos(θ) (I am going to use x instead of θ, it is just easier.
So, sin x / cos x is the numerator so far.
Lets deal with the denominator now.

Answer 2

1/cos x - cos x
Let's combine the fraction by making like denominators.
1/cos x-cos^2 (x)/cos(x)

Answer 3

You with me?

Answer 4

yes!

Answer 5

Awesome. The denominator fraction combines to (1-cos^2(x))/cosx.
1-cos^2(x) = sin^2(x)

Answer 6

So now, our denominator is simplified to sin^2(x)/cos(x).
We can flip the denominator fraction and multiply it by our numerator and cancel, to give 1/sin(x), which is csc(x).

Answer 7

thank you soooo much!!!

Answer 8

No problem :)