How do you prove tantheta-cottheta=(sectheta-csctheta)(sintheta+costheta)?

1 Answer
Sep 18, 2016

Please see below.

Explanation:

tantheta-cottheta

= sintheta/costheta-costheta/sintheta

= (sin^2theta-cos^2theta)/(costhetasintheta)

= ((sintheta-costheta)(sintheta+costheta))/(costhetasintheta)

= (sintheta+costheta)xx(sintheta-costheta)/(costhetasintheta)

= (sintheta+costheta)xx(sintheta/(costhetasintheta)-costheta/(costhetasintheta))

= (sintheta+costheta)xx(1/costheta-1/sintheta)

= (sintheta+costheta)(sectheta-csctheta)

= (sectheta-csctheta)(sintheta+costheta)