Simplify: (sin θ - cos θ)2 - (sin θ + cos θ)2

Solution:

Given expression is

(sin θ - cos θ)2 - (sin θ + cos θ)2

We have (a - b)2 = a2 - 2ab + b2 and (a + b)2 = a2 + 2ab + b2

{sin2θ - 2sinθcosθ + cos2θ} - {sin2θ + 2sinθcosθ + cos2θ}

{sin2θ - 2sinθcosθ + cos2θ - sin2θ - 2sinθcosθ - cos2θ}

The terms gets cancelled and the result would be -4sinθ cosθ .

Simplify: (sin θ - cos θ)2 - (sin θ + cos θ)2

Summary:

(sinθ - cosθ)2 - (sinθ +cosθ)2 is simplified as -4sinθ cosθ .

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