[(dy)/(dx)+2y=sin x*sec8x],[" (a) "y=5(2sin x-cos x)+ce^(2x)],[" (b) "y=(2sin x-cos x)+ce^(-x)],[" (c) "y=(2cos x-sin x)+ce^(2x)]

(cos x- cos y) ^(2) + (sin x - sin y) ^(2) =4 sin ^(2) "" ( x-y)/(2)

(cos x- cos y) ^(2) + (sin x - sin y) ^(2) =4 sin ^(2) "" ( x-y)/(2)

(cos x- cos y) ^(2) + (sin x - sin y) ^(2) =4 sin ^(2) "" ( x-y)/(2)

(cos x- cos y) ^(2) + (sin x - sin y) ^(2) =4 sin ^(2) "" ( x-y)/(2)

(cos x- cos y) ^(2) + (sin x - sin y) ^(2) =4 sin ^(2) "" ( x-y)/(2)

(dy) / (dx) -y cos x = 2x sin x

(dy) / (dx) = (sin x-sin y) (cos x) / (cos y)

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

Solutions of the differential equations (dy)/(dx) + (y)/(x) = sin x is : a) x(y+cos x ) = sin x+ c b) x(y-cos x ) = sin x+c c) x( y cos x ) = sin x +c d) x(y-cos x) = cos x+ c

Prove that (i) 2 cos x cos y=cos (x+y)+cos (x-y) (ii) -2 . sin x sin y=cos (x+y)-cos (x-y) (iii) 2 sin x cos y=sin (x+y)+sin (x-y) (iv) 2 cos x sin y=sin (x+y)-sin (x-y)