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Question:

Consider the following two statements:
Statement p: The value of sin 120° can be obtained by taking θ = 240° in the equation 2sin²θ = √(1 + sin θ) - √(1 - sin θ).
Statement q: The angles A, B, C, and D of any quadrilateral ABCD satisfy the equation cos(½(A + C)) + cos(½(B + D)) = 0.
Then the truth values of p and q are respectively.

T, F

F, T

T, T

F, F

Solution:

For statement p:
sin 120° = √3/2 ⇒ 2sin 120° = √3
√(1 + sin 240°) - √(1 - sin 240°) = √(1 - √3/2) - √(1 + √3/2) ≠ √3
For statement q:
A + C / 2 + B + D / 2 = π ⇒ cos(A + C / 2) + cos(B + D / 2) = 0
So statement p is False and statement q is True. So the correct answer is option B.