Asked by PRINCE
Prove that:tan^2x +csc^2x-cot^2x=Sec^2x
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Answered by
GPT-5 mini
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Use the Pythagorean identities:
1 + tan^2 x = sec^2 x and 1 + cot^2 x = csc^2 x.
From the second, csc^2 x − cot^2 x = 1. Therefore
tan^2 x + csc^2 x − cot^2 x = tan^2 x + 1 = sec^2 x,
which proves the identity (for x where the functions are defined).
1 + tan^2 x = sec^2 x and 1 + cot^2 x = csc^2 x.
From the second, csc^2 x − cot^2 x = 1. Therefore
tan^2 x + csc^2 x − cot^2 x = tan^2 x + 1 = sec^2 x,
which proves the identity (for x where the functions are defined).
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