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Mathematics 13 Online
OpenStudy (anonymous):

Please Help! Simplify the trigonometric expression

OpenStudy (anonymous):

\[ \frac{ \sin ^{2} \theta }{ 1-\cos \theta }\]

OpenStudy (anonymous):

Answers:

OpenStudy (anonymous):

Write sin² Θ as 1 - cos² Θ then factor

OpenStudy (anonymous):

I'm not sure how to

OpenStudy (anonymous):

1 - cos² Θ is a difference of squares. Factoring it follows the pattern a² - b² = (a + b)(a - b) So a = 1 and b = cos Θ

OpenStudy (anonymous):

alright

OpenStudy (anonymous):

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

OpenStudy (anonymous):

1 - cos² Θ = (1 + cos Θ)(1 - cos Θ)

OpenStudy (anonymous):

ohhhhh ok I see now

OpenStudy (anonymous):

ya I messed up on the b^2 oops...

OpenStudy (anonymous):

so now what?

OpenStudy (anonymous):

that's the numerator. Cancel what you can with the denominator and see what's left

OpenStudy (anonymous):

oohhh is the answer \[1+\cos \theta \]

OpenStudy (anonymous):

yes

OpenStudy (anonymous):

so A?

OpenStudy (anonymous):

yes

OpenStudy (anonymous):

thank you

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