How do you verify (1+csc(x))/(cot(x)+cos(x)) = sec(x)?
1 Answer
May 21, 2016
On the left side,
(1+cscx)/(cotx+cosx)
Rewrite
=(1+color(blue)(1/(sinx)))/(color(purple)((cosx)/(sinx))+cosx)
Simplify.
=((sinx+1)/(sinx))/((cosx+sinxcosx)/(sinx))
=(sinx+1)/(sinx)*(sinx)/(cosx+sinxcosx)
=(sinx+1)/(color(red)cancelcolor(black)(sinx))*(color(red)cancelcolor(black)(sinx))/(cosx+sinxcosx)
=(sinx+1)/(cosx+sinxcosx)
Factor out
=(sinx+1)/(cosx(1+sinx))
Simplify.
=color(red)cancelcolor(black)(sinx+1)/(cosxcolor(red)cancelcolor(black)((1+sinx)))
=1/cosx
=secx