Question

I don't understand how to do these particular ones? can someone help? I get the basic steps but I always get stuck.


(sin^2ө- Tan^2ө)/ (1-sec^2ө)

(secө-Tanө)^2 (1+sinө)-1

Answer 1

In most cases I suggest changing everything to sines and cosines, but sometimes the variations of the
Pythagorean identities come in handy

that is, by dividing sin^2 A + cos^2 A = 1 by cos^2 A we get
tan^2 A + 1 = sec^2 A

so the denominator of the first one is -tan^2 e
and the expression is
(sin^2 e - tan^2 e)/(-tan^2 e)
= sin^ e/-tan^2 e + tan^2 e/tan^2 e
= -cos^2 e + 1
= -sin^2 e

Answer 2

last line should be
= + sin^2 e

Answer 3

for the second one, I did change to sines and cosines
and got it to reduce to

(1-sin e)/(1+sin e)^2

I don't know how much further you have to go