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!