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Question
Prove the following trigonometric identities:
sin2 A cot2 A + cos2 A tan2 A = 1
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Solution
We have to prove `sin^2 A cot^2 A + cos^2 A tan^2 A = 1`
We know that `sin^2 A + cos^2 A = 1`
So,
`sin^2 A cot^2 A + cos^2 A tan^2 A = sin^2 A (cos^2 A)/(sin^2 A) + cos^2 A(sin^2 A)/(cos^2 A)`
`= cos^2 A + sin^2 A`
= 1
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