Answer:
Proven
Step-by-step explanation:
The given identity is
[tex]\frac{1-sin^2\beta }{cos^2\beta -1}=-cot^2\beta[/tex]
We use the fundamental trigonometric relationship
[tex]sin^2x+cos^2x=1[/tex]
Or equivalently
[tex]sin^2x=1-cos^2x[/tex]
[tex]cos^2x=1-sin^2x[/tex]
Using them in the left hand side
[tex]\frac{1-sin^2\beta }{cos^2\beta -1}=\frac{cos^2\beta }{-sin^2\beta}=-\left ( \frac{cos\beta }{sin\beta} \right )^2=-cot^2\beta[/tex]
Hence proven
