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Mathematics - Trigonometry - Identities

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Prove the following Identities:

Prove the following Identities:

1. tan² A / sec² A = 1 - cot ² A / csc² a

2. 1 / 1 - cos A tan A = cot A / cot A - cos A

3. cos² A ( 1 - sec² A) / cot² A sin² A - 1 = 1

4. (cot A = tan A) ² = sec² B csc² B°

Where A + B = 90°

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(1) LHS = tan^2 A / sec^2 A = (sin^2 A / cos^2 A) / (1 / cos^2 A) = sin^2 A
RHS = 1 - cot^2 A / csc^2 A = 1 - [(cos^2 A / sin^2 A) / (1 / sin^2 A)] = 1 - cos^2 A = sin^2 A
LHS = RHS

(2) LHS ...

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