Simplify the (sin θ - cos θ)2 + (sin θ + cos θ)2
Solution:
Given (sin θ - cos θ)2 + (sin θ + cos θ)2
This is of the form a2 - 2ab + b2 = (a - b)2 and a2 + 2ab + b2 = (a + b)2
sin2θ - 2sin θ cos θ + cos2θ + sin2θ + 2 sin θ cos θ + cos2θ
2sin2θ + 2cos2θ
2(sin2θ +cos2θ)
We have the trigonometric identity: sin2θ + cos2θ = 1
2(1) = 2
Simplify the (sin θ - cos θ)2 + (sin θ + cos θ)2
Summary:
(sin θ - cos θ)2 + (sin θ + cos θ)2 simplified as 2.
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