How do you verify #1/(secx+1 )= cot^2xsecx-cot^2x#?
1 Answer
Mar 21, 2018
We seek to prove that:
# 1/(secx+1) -= cot^2x secx-cot^2x #
Consider the RHS:
# RHS = cot^2x secx-cot^2x #
# \ \ \ \ \ \ \ \ = cot^2x(secx-1) #
# \ \ \ \ \ \ \ \ = cot^2x(secx-1) (secx+1)/(secx+1) #
# \ \ \ \ \ \ \ \ = (1/tan^2x(sec^2x-1))/(secx+1) #
# \ \ \ \ \ \ \ \ = (1/tan^2x(tan^2x))/(secx+1) #
# \ \ \ \ \ \ \ \ = (1)/(secx+1) #
# \ \ \ \ \ \ \ \ = LHS \ \ \ \ QED#
