How do you prove # secx(csc^2x)-csc^2x = secx / (1 + cosx)#?

1 Answer
Apr 10, 2018

We have:

#csc^2x(secx- 1) = secx/(1 + cosx)#

#1/sin^2x(1/cosx- 1) = (1/cosx)/(1+ cosx)#

#1/(sin^2xcosx) - 1/sin^2x = 1/(cosx(1 + cosx))#

#(1 - cosx)/(sin^2xcosx) = 1/(cosx(1 + cosx))#

#(1 -cosx)/((1- cos^2x)cosx) = 1/(cosx(1+ cosx))#

#(1 -cosx)/((1 + cosx)(1 - cosx)cosx) = 1/(cosx(1 + cosx))#

#1/(cosx(1 + cosx)) = 1/(cosx(1 + cosx))#

As required.

Hopefully this helps!