Question

Simplify parenthesis 1 minus cosine theta parenthesis times parenthesis 1 plus cosine theta parenthesis divided by parenthesis 1 minus sine theta parenthesis times parenthesis 1 plus sine theta parenthesis.

sin2 Θ
cos2 Θ
tan2 Θ
cosine theta over sine theta

Answer 1

heres an easier view:

Answer 2

@hartnn Please help again! aha

Answer 3

@phi @satellite73

Answer 4

@Compassionate @SolomonZelman @SithsAndGiggles

Answer 5

@TheSmartOne

Answer 6

@perl @sangya21

Answer 7

@camerondoherty @campbell_st @sammixboo @Nnesha

Answer 8

\[\frac{ (1 - \cos \theta)(1+ \cos \theta )}{ (1-\sin \theta)(1+\sin \theta ) } = \frac{ 1-\cos^2\theta }{ 1 - \sin^2 \theta }\]
\[\frac{ (1-\cos^2\theta }{ 1 - \sin^2 \theta } =\frac{ \sin^2 \theta }{ \cos^2 \theta}\]

Answer 9

so looking at the numerator

\[(1 - \cos(\theta))(1 + \cos(\theta))\]

which is the difference of 2 squares

and can be expanded to

\[1 - \cos^2(\theta)\]

then look at the denominator

the difference of 2 squares again

\[(1 - \sin(\theta)(1 + \sin(\theta))\]

I'll let you simplify that...

and lastly you will need the trig identity

\[\sin^2(\theta) + \cos^2(\theta) = 1\]

you will need use this to simplify the numerator and denominator.

hope it helps

Answer 10

I'm sorry, I'm completely confused when it comes to this stuff. I learn when I can see the answer and then it makes sense of how to work it out, would you mind giving me the answer from the answer choices? Thank you so much for all of your help already! @campbell_st

Answer 11

the role of open study is to help understanding, and not to provide answers. Look at the information posted by @sangya21 it is a basic identity

Answer 12

I fully understand, I know that the choices will either be A or D but I am not quite sure how to get there.. I'm so sorry if you feel as though I'm just cheating but I'm sincerely trying to learn this information. @campbell_st

Answer 13

\[\frac{ \sin \theta }{ \cos \theta }= \tan \theta\]
so what will be the ans?

Answer 14

\[\tan^2\Theta\] ???

Answer 15

@sangya21

Answer 16

correct

Answer 17

thank you so much!

Answer 18

anytime :)