Prove that (SinA-cosecS)^2+(cosA+secA)^2=3tan^2A+cot^2A
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question is wrong .... is should be ( 7 + tan^2A + cot^2A........
solution....
LHS
( sin A + cosec A) ^2 + ( cos A + sec A) ^2
= sin^2 A + cos^2 A + 2 sin A* cosec A + cos^2 A + sec^2 A + cos^2 A * sec^2 A
= sin^2 A + cot^2 A + 1 + 2 sin A * 1 / sin A + cos^2 A + tan^2 A + 1 + 2 cos^2 A * 1 / cos A
= sin^2 A + cos^2 A + cot^2 A + tan^2 A + 1 + 2 + 1 + 2
= 1 + cot^2 A + tan^2 A + 6
= 7 + tan^2 A + cot^2 A = RHS
solution....
LHS
( sin A + cosec A) ^2 + ( cos A + sec A) ^2
= sin^2 A + cos^2 A + 2 sin A* cosec A + cos^2 A + sec^2 A + cos^2 A * sec^2 A
= sin^2 A + cot^2 A + 1 + 2 sin A * 1 / sin A + cos^2 A + tan^2 A + 1 + 2 cos^2 A * 1 / cos A
= sin^2 A + cos^2 A + cot^2 A + tan^2 A + 1 + 2 + 1 + 2
= 1 + cot^2 A + tan^2 A + 6
= 7 + tan^2 A + cot^2 A = RHS
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