Question

Can anyone help me with number 9?

Answer 1

Sin x

Explanation:

I'm going to use x to represent theta.

1) Convert all of your trig ratios in terms of sin and cos:

`csc x - cot x * cos x`

=
`(1)/(sinx)` -
`(cosx)/(sinx)` *
`cos x`

2) Multiply first:

`(1)/(sin x) - (cos^(2)x )/(sin x)`

3) Combine the terms based on common denominator:

`(1- cos^(2)x )/(sin x)`

4) Using Pythagorean identities, substitute
`1 - cos^(2)x` for
`sin^(2)x`:

`(sin^(2)x )/(sin x)`

5) Simplify the fraction:

`(sin x * sin x)/(sin x)`

=
`sin x`