Question

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Prove that (tan theta + 1/cos theta)²+( tan theta - 1/cos theta)²=2 (1+ sin² theta)/(1- cos ² theta)​

Answer 1

Answer:

LHS = (tan + sec)^2 + (tan - sec)^2=

tan^2 + sec^2 +2tan.sec + tan^2 + sec^2 - 2tan.sec = 2(tan^2 + sec^2)

=2(sin^2+1/cos^2)

=2(sin^2 + 1)/cos^2= 2(1+sin^2)/(1-sin^2) = RHS

put theta in all cases