Given:
The expression is (sin θ + cos θ)2 + (sin θ - cos θ)2.
Solution:
(sin²θ + 2sinθcosθ + cos²θ) + (sin²θ - 2sinθcosθ + cos²θ)
= (sin²θ + cos²θ + 2sinθcosθ) + (sin²θ + cos²θ - 2sinθcosθ)
= sin²θ + cos²θ + sin²θ + cos²θ
= 2(sin²θ + cos²θ)
Identity sin²θ + cos²θ = 1:
= 2(1)
Therefore, the value of the expression is 2.
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