Question
If sin θ + cos θ = 1.2, find the value of sin θ. cos
θ.Solution
We know: sin² θ + cos² θ = 1 (Pythagoras identity). Given: sin θ + cos θ = 1.2. Let sin θ = x and cos θ = y. Then: x + y = 1.2, and x² + y² = ? Using the identity: (x + y)² = x² + y² + 2xy. 1.2² = x² + y² + 2xy. 1.44 = x² + y² + 2xy. From the Pythagoras identity: x² + y² = 1. Substitute into the equation: 1.44 = 1 + 2xy. 2xy = 1.44 - 1 = 0.44. xy = 0.44/2 = 0.22
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