Question

Question #603e4

Answer 1

You need to multiply out the brackets and use `cos^2 x+sin^2 x=1` and `tan x = sin x/ cos x`

Explanation:

`(1-cos x)(1+1/(cos x))`
Multiply out the brackets:
`=1 xx 1 -1 * cosx +1xx1/(cos x) - (cos x)/(cos x )`
`=1-cos x +1/(cos x)-1`
Cancel the `1`'s:
`=-cos x + 1/(cos x)`
Put over a common denominator:
`=(-cos^2 x+1)/(cos x)`
Use Pythagoras: `cos^2 x + sin^2 x = 1`
`=sin^2x/cosx`

`=(sin x xx sin x)/cos x`
Use `tan x = sin x /cos x`
`=tan x sin x`