Find the value of cot² B-cosec² B for 0 <B<90°.

Given: 

To find: $$\cot^2B-\cosec^2B$$ 

Formula Used: 

​$$\cot B = \frac{\cos B}{\sin B} , \ \ \ \cosec B = \frac{1}{\sin B} \\ \ \\ \sin^2 B + \cos^2 B = 1$$ 

Solution: 

Solving the expression;

​$$\cot^2B-\cosec^2B\\ = \frac{\cos^2 B}{\sin^2 B} - \frac{1}{\sin^2 B} \\ \ \\ = \frac{ \cos^2 B -1}{\sin^2 B} \\ \ \\ = \frac{ -( 1 - \cos^2B)}{\sin^2 B} \\ \ \\ =\frac{ - \cancel\sin^2 B}{\cancel\sin^2 B} = -1$$  

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