how do I simplify?

Question

(secө/ (secө-tanө)) - secөtanө

Answer 1

I usually switch everything to sines and cosines

(secө/ (secө-tanө)) - secөtanө
= (1/cosө) / (1/cosө - sinө/cosө) - (1/cosө)(sinө/cosө
= 1/(1 - cosө) - sinө/cos^2ө
= 1/(1 - cosө) - sinө/(1 - sin^2ө)
= 1/(1 - cosө) - sinө/((1 - sinө)(1 + sinө))
= (1 + sinө - sinө)/((1 - sinө)(1 + sinө))
= 1/cos^2ө