Solve in terms of sine and cosine:

Question

sec(x) csc(x)- sec(x) sin(x)

so far I have:
1/cos(x) 1/sin(x) - 1/cos(x) sin(x)

I am not sure where to go to from there. The book says the answer is cot(x) or cos(x)/sin(x)

Thank you in advance.

Answer 1

sec(x) csc(x)- sec(x) sin(x)
= (1/cos x)(1/sinx) - sinx/cosx
= [(1/sinx)-sinx]/cos x
= [1 - sin^2x]/(sin x cos x)
= cos^2 x/(sin x cos x)
= cosx/sinx = cot x

Answer 2

Dang, I see where I messed up. Thank you so much.

Answer 3

whoops, sorry everyone. The original message was supposed to be a reply to another post.