Question

(sin a + cos a )^2 + (sin a - cos a )^2 = ?

Answer 1

(sin a + cos a )^2 + (sin a - cos a )^2 =

sin²a+2sinacosa +cos²a +sin²a-2sinacosa +cos²a =2(sin²a+cos²a) =2·1=2

Answer 2

   
[tex]\displaystyle\\ (\sin a + \cos a )^2 + (\sin a - \cos a )^2 = \\\\ =(\sin^2 a +2\sin a \cdot \cos a + \cos^2 a )+ (\sin^2 a -2\sin a \cdot \cos a +\cos^2 a ) = \\\\ =\sin^2 a + \cos^2 a + \sin^2 a +\cos^2 a +\underbrace{2\sin a \cdot \cos a -2\sin a \cdot \cos a}_{\boxed{=0}}=\\\\ =\underbrace{\sin^2 a + \cos^2 a}_{\boxed{=1}} +\underbrace{ \sin^2 a +\cos^2 a}_{\boxed{=1}} = 1 + 1 = \boxed{\boxed{2}} [/tex]