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Prove.

\(\sec^2 a + cosec ^ 2 a = Sec^2 a. Cosec^2 a\)

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Proof ::

LHS = sec2 A + cosec2 A 

\(={1\over(cos^2A)}+{1\over(sin^2A)}={(sin^2A+cos^2A)\over(cos^2A sin^2A)}\) 

\(={1\over(cos^2A sin^2A)}=sec^2A cosec^2A=RHS\)

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