Answer
Please refer to the step-by-step part to see the detailed solution.
Work Step by Step
RECALL:
(1) $(a-b)(a+b) = a^2-b^2$
(2) $1 - \cos^2{\theta}=\sin^2{\theta}$
Use rule (1) above with $a=1$ and $b=\cos{\theta}$ to obtain:
$(1-\cos{\theta})(1+\cos{\theta})
\\=1^2 - \cos^2{\theta}
\\=1 -\cos^2{\theta}$
Use rule (2) above to obtain:
$1-\cos^{\theta}=\sin^2{\theta}$
Thus, the left side of the equation is equal to the right side of the equation.
The statement is true.