Question

Let O(0, 0) and C(π,0) be the given points. If least and the greatest value of x satisfies the equation cos2x = |sin x| = in (-π/2,π)in  represents the points A and B, respectively, then

(A)  OABC is a rhombus

(B)  OABC is a parallelogram

(C) OB = AC

(D)  area of a quadrilateral OABC is π/2 sq. units.

Answer 1

Correct option (B, D)

 

cos 2x = |sin x| ⇒ x = π/6 ,π/6, 5π/6

 That is,  A = (-π/6,1/2)

and  B = (5π/6, 1/2)

Clearly, AB = = OC π and AB ||OC

Also, OA = BC and OA|| BC

That is, OABC is a parallelogram.

Area OABC = π.1/2 = π/2sq. units