How to simplify cos x cos y(tan x + tan y)?

Question

I don't even understand what to do. Do i distribute both of the cos separately or independently? Someone, please show me the easiest way.

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Answer 1 · 2018-01-27T15:44:56

We can simplify to $sin(x + y)$

I would start by rewriting in terms of sine and cosine.

$=cosxcosy(sinx/cosx + siny/cosy)$

Now distribute and cancel.

$=cosysinx + cosxsiny$

Now this is familiar. Recall that $sin(A + B) = sinAcosB + cosAsinB$ .

$=sin(x +y)$

Hopefully this helps!