Question

Cos(x)(csc(x)+tan(x)) list steps

I just need every step, answer is not important. If you could explain each step, that would be awesome! one or two words is fine.

Answer 1

`\displaystyle \cos x \left(\csc x + \tan x\right) = \cot x + \sin x`

Explanation:

We want to simplify:

`\displaystyle \cos x \left(\csc x + \tan x\right)`

Recall that csc x = 1 / sin x and tan x = sin x / cos x. Substitute:

`\displaystyle = \cos x \left((1)/(\sin x) + (\sin x )/(\cos x)\right)`

Distribute:

`\displaystyle = (\cos x)/(\sin x) + (\cos x \sin x)/(\cos x) \\ \\ \\ = (\cos x)/(\sin x) + \sin x`

Recall that cot x = cos x / sin x. Hence:

`\displaystyle = \cot x + \sin x`

In conclusion:

`\displaystyle \cos x \left(\csc x + \tan x\right) = \cot x + \sin x`