Given `2 sin x+3 cos y =3,3siny+2cosx=4;(x , y in (0,pi/2))` then

If (sin x)/(sin y)=1/2, (cos x)/(cos y)=3/2 = 3/2 , where x, y in (0,pi/4) , then the value of tan(x+y) is equal to:

If (sin x)/(sin y)=(1)/(2), (cos x)/(cos y)=(3)/(2) , where x,y in (0,(pi)/(4)) , then the value of tan (x + y) is equal to

Find the particular solution of the differential equation cos x (dy/dx) + y sin x = 4x cos^2 x, (x ne pi/2) given that y = 3, x = 0

If (sinx)/(siny)=(1)/(2),(cosx)/(cosy)=(3)/(2) , where x,y in (0,(pi)/(2)) , then the value of tan (x+y) is equal to

If y=y(x) is the solution of the equation e^(sin y) cos y""(dy)/(dx) +e^(sin y) cos x = cos x,y (0)=0, then 1+y ((pi)/(6)) +( sqrt(3))/(2) y((pi)/(3)) +(1)/( sqrt(2)) y((pi)/(4)) is equal to

Consider the system of equations x cos ^(3) y + 3 x cosy sin^(2) y = 14 t o (1) and x sin^(3) y + 3 x cos^(2) y sin y = 13 to (2) The number of values of y in [0, 6 pi] are

Given, x cos^(3)y + 3x cosy sin^(2)y =14 and xsin^(3)y + 3x cos^(2)y siny=13 . The values of x -