Question

How do I simplify (sinx/(1-cosx))-cscx ?

Answer 1

`(sinx/(1-cosx))-cscx =cotx`

Explanation:

We know that,

`color(red)((1)1-cos^2theta=sin^2theta`

`color(blue)((2)cscx=1/sinx`

`color(violet)((3)cotx=cosx/sinx`

Here,

`(sinx/(1-cosx))-cscx =(sinx/(1-cosx)xx(1+cosx)/(1+cosx))-cscx`

`color(white)((sinx/(1-cosx))-cscx) =(sinx(1+cosx))/color(red)((1-cos^2x))-cscx`

`color(white)((sinx/(1-cosx))-cscx )=(sinx(1+cosx))/color(red)(sin^2x)-cscxtoApplycolor(red)((1)`

`color(white)((sinx/(1-cosx))-cscx )=(1+cosx)/sinx-cscx`

`color(white)((sinx/(1-cosx))-cscx) =cancel(1/sinx)+cosx/sinx-cancel(1/sinx)toApplycolor(blue)((2)`

`color(white)((sinx/(1-cosx))-cscx) =cosx/sinx...toApplycolor(violet)((3)`

`(sinx/(1-cosx))-cscx =cotx`