If Sin θ (1 + Sin θ) + Cos θ (1 + Cos θ) = x and Sin θ (1 – Sin θ) + Cos θ (1 – Cos θ) = y then

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Question

If sin θ (1 + sin θ) + cos θ (1 + cos θ) = x and sin θ (1 – sin θ) + cos θ (1 – cos θ) = y then

easy

Solution

Correct option is

x – y = 2

sin θ + cos θ = x – 1 = y + 1

sin 2θ = (sin θ + cos θ)² – 1 = x² – 2x = y² + 2y

xy = (sin θ + cos θ)² – 1 = sin 2θ

x – y = 2

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