SOLUTION: To which of the following expressions is the expression (1-cosθ)(1+cosθ) equivalent to? A. 1 B. sin^2θ C. csc^2θ D. cos^2θ E. sin^2θ

Algebra ->  Trigonometry-basics -> SOLUTION: To which of the following expressions is the expression (1-cosθ)(1+cosθ) equivalent to? A. 1 B. sin^2θ C. csc^2θ D. cos^2θ E. sin^2θ      Log On


   

Question 1197788: To which of the following expressions is the expression (1-cosθ)(1+cosθ) equivalent to?
A. 1
B. sin^2θ
C. csc^2θ
D. cos^2θ
E. sin^2θ
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%281-cos%28theta%29%29%281%2Bcos%28theta%29%29

= %281%5E2-cos%5E2%28theta%29%29

= 1-cos%5E2%28theta%29..........using identity sin%5E2%28theta%29%2Bcos%5E2%28theta%29=1
= sin%5E2%28theta%29

answer: sin%5E2%28theta%29
note: you have two options, B and E, unless you made typo
whatever is sin%5E2%28theta%29 is your answer

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Use the difference of squares rule, and pythagorean identity, to say
%281-cos%28theta%29%29%281%2Bcos%28theta%29%29+=+1-cos%5E2%28theta%29+=+sin%5E2%28theta%29

Therefore,
%281-cos%28theta%29%29%281%2Bcos%28theta%29%29+=+sin%5E2%28theta%29
is an identity. It is a true equation for all real numbers theta.

You mention sin%5E2%28theta%29 twice (choices B and E)

I have a feeling one of those is supposed to be sin%282theta%29, but I'm not 100% sure.