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let me take teta=A ( cos^2(90-A) =Sin^2 A)
sec^2 A- cot^2(90-A)= sin^2 A +cos^2 A
1/cos^2 A - sin^2 A/cos^2A =1
1-sin^2A/cos^2A=1
1-sin^2 A= cos^2 A
sin^2 A+ cos ^2 A =1
1=1
hence proved
Hope it helps you
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