(Q12)Evaluate the following:

ii. (sin θ + cos θ)2 + (sin θ – cos θ)2

Given (sin θ + cos θ)2 + (sin θ – cos θ)2

= (2 θ + 2 θ + sin θ cos θ) + (2 θ + 2 θ – sin θ cos θ)

[∵ (a + b)2 = a2 + b2 + 2ab,(a – b)2 = a2 + b2 – 2ab]

= + sin θ cos θ + – sin θ cos θ

[∵ sin2 θ + cos2 θ = 1]

= +

=