# How do you simplify #(tan x + cos x +sin x tan x)/ (sec x + tan x)#?

##### 1 Answer

Always remember your basic identities:

#cos^2(x)+sin^2(x)=1# #tan(x)=sin(x)/cos(x)# #sec(x)=1/cos(x)#

There are (many) others, but these are the most fundamental for trigonometry. In fact, *every* simple trigonometric function can be written in terms of sines and cosines. For example, the scary-looking "half coversed cosine" hacovercos(x) (which is not usually examinable) is simply

Using the above identities, suddenly your equation becomes:

From this point, it's algebraic manipulation and not much else more.