Question

PROVE:

cos t / 1 + sin t = 1 - sin t / cos t

Answer 1

Do you know your trig identities?

Answer 2

i have em right here in front of me but iunno where to begin

Answer 3

multiply both numerator and deonom by 1-sint and get ur result

Answer 4

one thing with proving identities is that you start with whatever side looks more complicated to you and you basically simplify to the other side.

in this case, you could've also worked from the right side and simplified to get the left side.

Answer 5

multiply 1 - sin t on which side???

Answer 6

rationalize the denominator then use the formula tha 1-sin^2t=cos^2t

Answer 7

Do you remember in surds when we had to rationalise this?
\[\frac{1}{\sqrt{2}-1}\]
What did we do? We multiplied top and bottom by its conjugate, as so:
\[\frac{1}{\sqrt{2}-1}\times\frac{\sqrt{2}+1}{\sqrt{2}+1}\]
to get:
\[\sqrt{2}+1\]
Sometimes in trig, we need to do the same thing.
So in this case, multiply top and bottom of LHS by 1 - sin(t) to get
1-sin^2(t) in the bottom, which as we know is = to cos^2(t)
cos(t) cancels in top and bottom to get RHS