If θ lies in the fourth quadrant and 3 cot θ + 4 = 0, then what is the value of sin 2θ + cos 2θ?
A.-31/25
B.-17/25✓ Correct
C.0
D.1
Explanation
cot θ = -4/3, so tan θ = -3/4. In Q4, sin θ = -3/5, cos θ = 4/5. sin 2θ = 2 sin θ cos θ = 2(-3/5)(4/5) = -24/25. cos 2θ = cos²θ - sin²θ = 16/25 - 9/25 = 7/25. Sum = -24/25 + 7/25 = -17/25.
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