Answer:
Sin x
Step-by-step explanation:
I'm going to use x to represent theta.
1) Convert all of your trig ratios in terms of sin and cos:
[tex]csc x - cot x * cos x[/tex]
=[tex]\frac{1}{sinx}[/tex] - [tex]\frac{cosx}{sinx}[/tex] * [tex]cos x[/tex]
2) Multiply first:
[tex]\frac{1}{sin x} - \frac{cos^{2}x }{sin x}[/tex]
3) Combine the terms based on common denominator:
[tex]\frac{1- cos^{2}x }{sin x}[/tex]
4) Using Pythagorean identities, substitute [tex]1 - cos^{2}x[/tex] for [tex]sin^{2}x[/tex]:
[tex]\frac{sin^{2}x }{sin x}[/tex]
5) Simplify the fraction:
[tex]\frac{sin x * sin x}{sin x}[/tex]
=[tex]sin x[/tex]
