Listen NCERT Audio Books to boost your productivity and retention power by 2X.
Choose the correct answer
If , then 9x2 – 12xy cos θ + 4y2 is equal to
We are given with,
We need to find the value of 9x2 – 12xy cos θ + 4y2.
Using property of inverse trigonometry,
Take Left Hand Side (LHS) of:
Replace A by and B by
.
Further solving,
We shall equate LHS to RHS,
Taking cosine on both sides,
Using property of inverse trigonometry,
cos(cos-1 A) = A
So,
By cross-multiplying,
⇒ xy - √(4 – x2) √(9 – y2) = 6 cos θ
Rearranging it,
⇒ xy – 6 cos θ = √(4 – x2) √(9 – y2)
Squaring on both sides,
⇒ [xy – 6 cos θ]2 = [√(4 – x2) √(9 – y2)]2
Using algebraic identity,
(a – b)2 = a2 + b2 – 2ab
⇒ (xy)2 + (6 cos θ)2 – 2(xy)(6 cos θ) = (4 – x2)(9 – y2)
⇒ x2y2 + 36 cos2 θ – 12xy cos θ = 36 – 9x2 – 4y2 + x2y2
⇒ x2y2 – x2y2 + 9x2 – 12xy cos θ + 4y2 = 36 – 36 cos2 θ
⇒ 9x2 – 12xy cos θ + 4y2 = 36 (1 – cos2 θ)
Using trigonometric identity,
sin2 θ + cos2 θ = 1
⇒ sin2 θ = 1 – cos2 θ
Substituting the value of (1 – cos2 θ), we get
⇒ 9x2 – 12xy cos θ + 4y2 = 36 sin2 θ