Prove. (cosA + sinA)^2 + (cosA - sinA)^2 = 2 - Vidyadip

Question

Prove.
$(cosA + sinA)^2 + (cosA - sinA)^2 = 2$

✓

Answer

$LHS =(cosA + sinA)^2 + (cosA - sinA)^2$
$= \cos^2A + \sin^2A + 2cos A.\sin A + \cos^2A + \sin^2A - 2cos A.\sin A$
$= 2(\cos^2A + \sin^2A) = 2 = RHS$

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