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Consider the following two statements. Statement p : The value of sin 120° can be divided by taking θ = 240° in the equation 2 sin(θ/2) = √(1+sinθ) - √(1-sinθ). Statement q : The angles A, B, C and D of any quadrilateral ABCD satisfy the equation cos(1/2(A + C)) + cos(1/2(B + D)) = 0 Then the truth values of p and q are respectively.

1. F, T
2. T, T
3. F, F
4. D, T

Correct answer: T, T

Solution

Both statements are true; statement p correctly applies the half-angle identity for sine, and statement q accurately reflects a property of the angles in a quadrilateral, confirming that the sum of the cosines of half the opposite angles equals zero.

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