PYQ - Prove the following identity II — task. Maths TNSB Mentoring, Class 10 Crash course.

Prove the following identites.

$\frac{1 - cot^2 \ C}{tan^2 \ C - 1} = cot^2 \ C$

Proof:

Answer variants:

$\frac{cos^2 \ C}{sin^2 \ C}$

$cot^2 \ C$

$\frac{sin^2 \ C}{cos^2 \ C}$

$tan^2 \ C$

$\begin{array}{l} LHS = \frac{1 - \cot^{2} C}{\tan^{2} C - 1} \\ = \frac{1 - i}{i - 1} \\ = \frac{\frac{\sin^{2} C - \cos^{2} C}{\sin^{2} C}}{\frac{\sin^{2} C - \cos^{2} C}{\cos^{2} C}} \\ = \frac{\cos^{2} C}{\sin^{2} C} \\ = i \end{array}$

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4. PYQ - Prove the following identity II

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