Question

cot²A - cot²B=sin²B-sin²A/sin²A. sin²B​

Answer 1

Step-by-step explanation:

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Answer 2

We know that $\cot A = \frac{\cos A}{\sin A}$.

Hence

$\cot^2A= \frac{\cos^2 A}{\sin^2 A}$

$\cot^2A-\cot^2B=\frac{1-\sin^2A}{\sin^2A} -\frac{1-\sin^2B}{sin^2B} \\\\\cot^2A-\cot^2B=\frac{\sin^2B-\sin^2B\sin^2A - \sin^2A +\sin^2A\sin^2B }{\sin^2A\sin^2B} \\\\\cot^2A-\cot^2B=\frac{\sin^2B - \sin^2A }{\sin^2A\sin^2B}$

Hence it is proved.

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