cos x + sin x tan x = sec x
One thing about verifying identities is that there may be more than one way to proceed. I always like to convert things to sines and cosines. where possible.
So, proceeding in that manner on the left side, we have:
cos x + (sin x) * ( (sin x) / (cos x) ) = sec x
cos x + ( (sin x)^2 / cos x ) = sec x
Getting a common denominator on the left, we have :
( (cos x ) ^2 + (sin x )^2 ) / cos x = sec x
Now, using the identity (cos x ) ^2 + (sin x )^2 = 1, we have
1/ cos x = sec x
sec x = sec x
Voila!!
Hopes this helps!!
