how do i go about solving a trig identity; that simplify s 1-sin^2 theta/1-cos theta

i know that sin^2 theta=1-cos^2 theta, but how do i express 1-cos theta, how do i simplify

Julie from Arvada, CO 10/11/2012

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Is the question 1- [(sin²T) / (1-cos T)] ?

Please clarify

- Gayathri J. 10/11/2012

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1 Answer

first, Simplify 1- cos²Θ= sin²Θ

We know the expression a²- b² = (a+b)( a- b)

Similarly, write the left hand side of the equation as (1+cos Θ)(1-cos Θ)

so the whole thing can be written as (1+cos Θ)(1-cos Θ)= Sin²θ

Divide both sides by (1-cos Θ)

-----> (1+cos Θ) = (Sin² θ)/ (1- cos θ)

Therefore, if the original question is 1- [(sin²Θ) / (1-cos Θ)] ,

then your answer will be 1 -(1+cos Θ) = - cos Θ

Gayathri J. 10/11/2012