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!
