5x cos y=sin(x+y)

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)

Show that (i) cos x+cos y=2 cos (x+y)/(2) cos (x-y)/(2) (ii) cos x-cos y=-2 sin (x+y)/(2) sin (x-y)/(2) (iii) sin x+sin y=2 sin (dot(x)+y)/(2) cos (x-y)/(2) (iv) sin x-sin y=2 cos (x+y)/(2) sin (x-y)/(2)

Prove that cos (x + y) = cos x cos y-sin x sin y

56.The value of cos^(2)x+cos^(2)y-2cos x cos y cos(x+y) is (A) sin(x+y) (B) sin^(2)(x+y) (C) sin(x+y) (D) sin(x+y)

Prove that |(1,x,y),(0, sin x, sin y),(0, cos x,cos y)|= sin (x-y)

What is the value of (sin (x-y))/(cos x cos y)+(sin (y-z))/(cos y cos z)+(sin (z-x))/(cos z cos x) ?

Prove geometrically that cos(x + y) = cos x cos y - sinx sin y and hence prove cos((pi)/(2) + x) = - sin x .

Prove that : (sin (x+y))/(sin (x-y) )= (sin x. cos y + cos x . Sin y)/(sin x. cos y-cos x. sin y)

Prove that : (sin (x+y))/(sin (x-y) )= (sin x. cos y + cos x . Sin y)/(sin x. cos y-cos x. sin y)

The value of (sin x cos y + cos x sin y)^2+(cos x cos y -sin x sin y)^2 is equal to