Precalc HELP PLEEEEASE:
Verify the identity
(1-sin(x))/cos(x)=cos(x)/(1+sin(x))

Question

psymon · Answer

Often times when you have something like a + sinx, b - cosx, or some sort of number +/- a trig function you need to multiply the top and bottom by a conjugate. We know what a conjugate is, correct?

anonymous · Answer

yes of course.. but can you tell me just so i know that you know what conjugates are :)

psymon · Answer

Lol, I see. Gotta test me, correct? Well a conjugate is when you take the same group but switch the sign in between. If you have a + b, then the conjugate is a - b. For you, you have 1-sin(x) in the numerator of your one fraction, so the conjugate would be 1+sin(x). SO I would start off with that left fraction and multiply the top and bottom by 1+sin(x).

anonymous · Answer

ah yes just what i was thinking. i would then arive at 1-sin^2(x)/cos(x)+cos(x)sin(x) correct?

psymon · Answer

Yes, you would. Now as a hint, don't distribute in the bottom. just have it as cos(1+sinx) in the denominator. Your numerator can be changedusing an identity. Think you see it?

anonymous · Answer

yes i knew it all along, thank you for confirming my suspicions.

psymon · Answer

Mhm. Glad you got it ^_^