How do you prove 1/(tanx-secx)-1/(tanx+secx)= -2secx ?

1 Answer
Jan 9, 2018

See below

Explanation:

#1/(tanx-secx)-1/(tanx+secx)#

#=(tanx+secx-tanx+secx)/(tan^2x-sec^2x)#

#=(2secx)/-1=-2secx#, as required. #square#

Note: Here we use #tan^2x-sec^2x=-1# which can be derived from the Pythagorean identity.