How do you verify #sinx/(1-cosx) - (sinxcosx)/(1+cosx)=cscx(1+cos^2x)#?
1 Answer
May 13, 2018
We have:
#(sinx(1 +cosx) - sinxcosx(1 - cosx))/((1 - cosx)(1 + cosx)) = cscx(1 + cos^2x)#
#(sinx + sinxcosx - sinxcosx + sinxcos^2x)/((1 - cosx)(1 +cosx)) = cscx(1 +cos^2x)#
#(sinx + sinxcos^2x)/(1 - cos^2x) = cscx(1 + cos^2x)#
#(sinx+ sinxcos^2x)/sin^2x = cscx(1 +cos^2x)#
#(sinx(1 + cos^2x))/sin^2x = cscx(1 +cos^2x)#
#cscx(1 + cos^2x) = cscx(1 + cos^2x)#
As required.
Hopefully this helps!
