How do I solve $(cot(x)+tan(x)) / (csc(-x))$ ?

Question

I assume I need to convert $cot(x) + tan(x)$ into terms of cosine and sine, then end up with $1/(sin(x)cos(x))$ , but I get stuck with how to deal with the rest of the problem from there.

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Answer 1 · 2017-10-14T15:55:07

This equals $-secx$ .

I like to rewrite in terms of sine and cosine.

$=(cosx/sinx + sinx/cosx)/(1/sin(-x))$

We also know that $sin(-x) = -sin(x)$ .

$= ((cos^2x+ sin^2x)/(cosxsinx))/(-1/sinx)$

We can use $sin^2x + cos^2x = 1$ , as you have done.

$= (1/(cosxsinx))/(-1/sinx)$

$= 1/(cosxsinx) * -sinx$

$= -1/cosx$

This can be rewritten using $secx = 1/cosx$ .

$=-secx$

Hopefully this helps!