Prove identity (cos A +SIN A)^2+ Cos A _SIN A)^2=2

1.	Prove identity (cos A +SIN A)^2+ Cos A _SIN A)^2=2
Answer» Answer: $(cos \: a + \: sin \: a)^{2} + (cos \: a \: - \: sin \: a \: )^{2} \\ = cos^{2} a \: + sin^{2} a \: + \: 2cos ^{2}a \: sin ^{2} a \: + \: cos^{2} a + \\ sin^{2} a - 2cos ^{2} a \: sin ^{2} a$ $we \: know \: that \: cos ^{2} a + sin ^{2} a = 1$ $also \: \\ 2 {cos}^{2} a \: {sin}^{2} a \: - 2 {cos}^{2} a \: {sin}^{2} a \: = 0$ There for we are LEFT with 1+1=2 HENCE proved HOPE this answer helps you !

Answer»

Answer:

$(cos \: a + \: sin \: a)^{2} + (cos \: a \: - \: sin \: a \: )^{2} \\ = cos^{2} a \: + sin^{2} a \: + \: 2cos ^{2}a \: sin ^{2} a \: + \: cos^{2} a + \\ sin^{2} a - 2cos ^{2} a \: sin ^{2} a$