" 1."2x+3y=sin x

2x + 3y = sin y

" 1.If sin x+sin y=(1)/(4),cos x+cos y=(1)/(3) then tan((x+y)/(2))=

If (tan x) / (tan y) = (1 + cos ^ (2) x) / (1 + sin ^ (2) x), show that sin (3x + y) = 7sin (xy)

If (tan x) / (tan y) = (1 + cos ^ (2) x) / (1 + sin ^ (2) x), show that sin (3x + y) = 7sin (xy)

Draw the graph of : y =f (x) =3 sin (2x -1) .

Find y ', if : (a) y=3 cos x + 2 sin x, (b) y=(sin x+cos x)/(sin x -cos x) (c ) y=(x^(2)+1) arc tan x, (d) y=x^(3) arc sin x

"If " (tan x)/(tan y) = (1 + cos^(2) x)/(1 + sin^(2) x ) " show that "sin ( 3x + y) =7sin (x-y).

(dy)/(dx)+(3x^(2))/(1+x^(3))y=(sin^(2)x)/(1+x^(3))

The solution of the differential equation (dy)/(dx) +(3x^(2))/(1+x^(3))y = (sin^(2) x)/(1+x^(3)), is