Question

How do you simplify this trig expression?

Answer 1

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

Answer 2

Hints: rewrite (sin theta)^2 in terms of cos theta.

apply this principle:\[\frac{ 1-g^2 }{ 1-g }=1+g\]

Answer 3

Awesome thanks! Would it be \[(\cos \theta)\]

Answer 4

@sshayer

Answer 5

no
you can solve either multiply each the numerator and denominator by 1- cos theta

Answer 6

or use \[\sin ^2 \theta+\cos ^2 \theta=1,\sin ^2 \theta=1-\cos ^2 \theta= \left( ? \right)\left( ? \right) \]

Answer 7

Ohhh really? Okay so I got \[(\sin ^2\theta)\]
but that's not an answer choice...

Answer 8

With what are you replacing (sin theta)^2? Be specific, please.

How would you ssimplify your result? Show all steps, please.

Answer 9

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

Answer 10

make factors of numerator.

Answer 11

I still think it's \[(1-\cos \theta)/(\cos \theta)\]

Answer 12

\[a^2-b^2=\left( a+b \right)\left( a-b \right)\]
\[1-\cos ^2\theta=1^2-\left( \cos \theta \right)^2=?\]
can you make factors now ?

Answer 13

a=1,b=cos theta

Answer 14

Bwahaha That makes sense thank you!

Answer 15

this is the key; apply this info to the problem at hand.\[1-\cos ^2\theta=1^2-\left( \cos \theta \right)^2=?\]

Answer 16

Hint: You've GOT TO FACTOR the right side of the equation above.

Answer 17

\[\theta=\pi/2, \pm \pi n, \pm2\pi n\]