Question

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` = `sqrt(1 + sin θ) - sqrt(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.

Options

• F, T

• T, T

• F, F

• T, F

Answer 1

F, T

Explanation:

Statement p:

sin 120° = cos 30° = `sqrt(3)/2`

⇒ 2 sin 120° = `sqrt(3)`

So, `sqrt(1 + sin240^circ) - sqrt(1 - sin 240^circ)`

 = `sqrt((1 - sqrt(3))/2) - sqrt((1 + sqrt(3))/2) ≠ sqrt(3)`

Statement q:

So, A + B + C + D = 2π

⇒ `(A + C)/2 + (B + D)/2` = π

⇒ `cos((A + C)/2) + cos((B + D)/2)`

= `cos((A + C)/2) - cos((A + C)/2)` = 0

Therefore, statement p is false and statement q is true.