" C-2."quad y=sin x cos x

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)

(e^(y)+1)cos x dx+e^(y)sin x dy =0 A) (e^(y)+1)sin x =c B) (e^(y)+1)=c tan x C) e^(y)sin x + cos x=c D) (e^(x)+1)sin y=c

If tan x=(2b)/(a-c),y=a cos^(2)x+2b sin x cos x+c sin^(2)xz=a sin^(2)x-2b sin x cos x+c cos^(2)x, that y-z=a-c.

xdx+secxdy=0, y=0" if " x=(pi)/(2) A) x+y cos y+cos y=(pi)/(2) B) y+x sin x-cosx=(pi)/(2) C) y+x sin x+cos x=(pi)/(2) D) x+y sin y+cos y=(pi)/(2)

If tan x= (2b)/(a-c), a!=c, y = a cos^2 x +2b sin x*cos x + c sin^2x, z = a sin^2 x-2b sin x*cos x + c.cos^2x, then

If quad tan x=(2b)/(a-c),a!=c,y=a cos^(2)x+2b sin x*cos x+c sin^(2)x,z=a sin^(2)x-2b sin x*cos x+c cos^(2)x, then

cos (x + y), sin (x + y), - cos (x + y) sin (xy), cos (xy), sin (xy) sin2x, 0, sin2y] | = sin2 (x + 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