Question

How do you simplify? cos x + tan x sin x

Answer 1

We have the following:

$\cos x+\tan x\cdot\sin x$

we simplify:

$\cos x+\frac{\sin x}{\cos x}\cdot\sin x=\cos x+\frac{\sin^2x}{\cos x}=\frac{\cos x\cdot\cos x}{\cos x}+\frac{\sin^2x}{\cos x}=\frac{\cos^2x}{\cos x}+\frac{\sin^2x}{\cos x}=\frac{\cos^2x+\sin^2x}{\cos x}=\frac{1}{\cos x}=\sec x$

Therefore

$\cos x+\tan x\cdot\sin x=\sec x$