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

Question

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

 

 

 

 

Answer 1

It's not clear what the problem is. It depends on where you may have some implicit parentheses

(1-sin^2T)/(1-cosT)

substitute this identity for 1

sin^2T + cos^2T = 1

to get

(sin^2T+cos^2T -sin^2T)/(1-cos^T)

=cos^2T/(1-cosT)

BUT if the problem is 1- sin^2T/(1-cosT) then

= 1 - (1-cos^2T)/(1-cosT) = 1 - (1+cosT) = -cosT

actually there's a 3rd possibility. The way it's written

reads 1- sin^2T/1 - cosT

that = 1 -sin^2T -cosT= cos^2T - cosT

= cosT(cosT-1)

odds are though you wanted the interpretation

that led to

-cosT

Answer 2

first, Simplify 1- cos² Θ= 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)= Sin² θ

 

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