How do I put "cos^2 theta" into the denominator of "1/1-sin theta"?
Multiply top and bottom by 1+sinθ:
1/(1-sinθ) * (1+sinθ)/(1+sinθ)
= (1+sinθ)/(1-sin^2θ)
= (1+sinθ)/cos^2θ
Thanks!! Why does it turn into cos^2 θ off of 1 + sinθ?
To put "cos^2 theta" into the denominator of "1/1-sin theta," you can multiply both the numerator and the denominator by "cos^2 theta".
Here's how you do it step by step:
1. Start with the fraction "1/1-sin theta" which has "1" as the numerator and "1-sin theta" as the denominator.
2. Multiply both the numerator and the denominator by "cos^2 theta". This is done to create a common denominator with the denominator of "cos^2 theta".
Numerator:
1 * cos^2 theta = cos^2 theta
Denominator:
(1 - sin theta) * cos^2 theta
3. Now your expression becomes "cos^2 theta / ((1 - sin theta) * cos^2 theta)".
That's how you can put "cos^2 theta" into the denominator of "1/1-sin theta" by multiplying both the numerator and the denominator by "cos^2 theta".