Question 1057127
Starting with the left side, combine 1/tan x and tan x into a single fraction.


You can do this by multiplying tax by (tan x / tan x):


{{{1/tan x + tan x = 1/tanx + (tan x)(tan x / tan x) = (1 + (tan x)^2)/ tan x }}}


Then, from {{{(sin x)^2 + (cos x)^2 = 1}}}, you can get {{{1 + (tan x)^2 = (sec x)^2)}}} 
by dividing through by {{{(cos x)^2}}}


Substituting {{{(sec x)^2}}} in place of {{{1 + (tan x)^2}}} gives:


{{{1/tan x + tan x =  ((sec x)^2)/(tan x)) }}}