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+(\sin x)/(\cos x)\cdot\sin x=\cos x+(\sin^2x)/(\cos x)=(\cos x\cdot\cos x)/(\cos x)+(\sin^2x)/(\cos x)=(\cos^2x)/(\cos x)+(\sin^2x)/(\cos x)=(\cos^2x+\sin^2x)/(\cos x)=(1)/(\cos x)=\sec x`

Therefore

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