" 3."cos(x+y)=cos x cos y-sin x sin y

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

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

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

(dy) / (dx) = - (cos x (3cos y-7sin x-3)) / (sin y (3sin x-7cos y + 7))

Prove that, cos 4 x - cos4 y = 8(cos x - cos y)(cos x + cos y)(cos x - sin x)(cos x + sin y)

If cos (x-y) =-1, then the values of (cos x+ cos y) and (sin x + sin y) are respectively-

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)

What ( sin x cos y + cos x sin y) (sin x cos y - cos x sin y) equal to ?