Question

prove cos x + sin x tan x= 1/cosx

Answer 1

take the left hand side...
\[\cos x + \sin x \tan x\]
change tanx to sinx/cosx
\[\implies \cos x + \sin x ( \frac{\sin x}{\cos x})\]
simplify
\[\implies \cos x + \frac{\sin^2 x}{\cos x}\]
change to common denominators
\[\implies \frac{\cos^2 x}{\cos x} + \frac{\sin^2 x}{\cos x}\]
add
\[\implies \frac{\cos^2 x + \sin^2 x}{\cos x}\]
now.. you know that cos^2 x + sin^2 x = 1 because of pythagorean identity
\[\implies \frac 1{\cos x} = RHS\]
does that help?