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Question
Prove the following trigonometric identities.
`(1 - tan^2 A)/(cot^2 A -1) = tan^2 A`
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Solution
`(1 - sin^2 A/cos^2 A)/(cos^2 A/sin^2 A -1) = ((cos^2 A - sin^2 A)/cos^2 A)/((cos^2 A - sin^2 A)/sin^2 A`
`= (sin^2 A)/cos^2 A`
`= tan^2 A`
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