(1+secA+tanA)(1-cosecA+cotA)=2 prove it.
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LHS - (1+sin A / cos A +1 / cos A).(1 + cos A / sin A - 1 / sin A)
= (cos A + sin A + 1) / cos A .(sin A + cos A - 1) / sin A
= (cos A + sin A) ^2 - 1 / sin A cos A
= 1 + 2 sin A cos A - 1 / sin A cos A
= 2 sin A cos A / sin A cos A
= 2
RHS - 2
Hence proved
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