Trigonometric EquationHard

Question

Differential equation of a curve is given by dx = by where x,y ∈ and curve passes through the point , then -

Options

A.equation of curve is sin(x + y) + sin(x - y) = 1
B.equation of curve is y = cos-1
C.curve does not intersect y-axis
D.equation of curve is y = cos-1

Solution

dx =
∵ x, y ∈ Ist quadrant
∴ cos y cosx dx = sinx siny dy
= cot x cot y
⇒ cot x dx
⇒ l n|sec y| = l n|sin x| + c
∵ it passes through
⇒ c = l n2
⇒ |secy| = 2|sinx|
⇒ 2 sinx cosy = 1 (∵ x, y ∈ Ist quadrant)
(A) sin(x + y) + sin(x - y) = 1
(B) cos y = ⇒ y = cos-1
(C) put x = 0 ⇒ 0 = 1
⇒ curve does not corss y - axis

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