Answer
$(1-\cos\beta)(1+\cos\beta)=\dfrac{1}{\csc^{2}\beta}$
Work Step by Step
$(1-\cos\beta)(1+\cos\beta)=\dfrac{1}{\csc^{2}\beta}$
Evaluate the product on the left side of the equation:
$1-\cos^{2}\beta=\dfrac{1}{\csc^{2}\beta}$
Substitute $1-\cos^{2}\beta$ with $\sin^{2}\beta$:
$\sin^{2}\beta=\dfrac{1}{\csc^{2}\beta}$
Since $\sin^{2}\beta=\dfrac{1}{\csc^{2}\beta}$, the identity is proved:
$\dfrac{1}{\csc^{2}\beta}=\dfrac{1}{\csc^{2}\beta}$
