Question

How do you prove `(sec x + tan x)(1 - sin x) = cos x` ?

Answer 1

See explanation...

Explanation:

Use:

`sec x = 1/cos x`

`tan x = sin x/cos x`

`cos^2 x + sin^2 x = 1`

Then:

`(sec x + tan x)(1 - sin x) = (1/cos x + sin x/cos x)(1- sin x)`

`color(white)((sec x + tan x)(1 - sin x)) = ((1+sin x)(1- sin x))/cos x`

`color(white)((sec x + tan x)(1 - sin x)) = (1-sin^2 x)/cos x`

`color(white)((sec x + tan x)(1 - sin x)) = cos^2 x/cos x`

`color(white)((sec x + tan x)(1 - sin x)) = cos x`