Prove that ( 1 + Tan A)2 + (1 - Tan A)2 = 2 Sec2a

Prove that ( 1 + tan A)² + (1 - tan A)² = 2 sec²A

Sum

LHS = ( 1 + tan A)² + (1 - tan A)²= 1 + 2 tan A + tan²A + 1 - 2 tan A + tan²A
= 2( 1 + tan²A)
= 2 sec²A
= RHS
Hence proved.

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