(pi)(sin2x-sin^(2)y)/(cos2y-cos2x)=cot(x+y)

prove that: (sin2x-sin2y)/(cos2y-cos2x)=cot(x+y)

(sin 2x - sin 2y)/(cos 2y-cos 2x) = cot (x+y)

If cot theta = cos (x+y) "and" cot phi = cos (x-y), "show that" tan (theta- phi)=(2sin x sin y )/(cos^(2) x + cos^(2) y)

Prove the following: cos(pi/2-x)cos(pi/2-y)-sin(pi/2-x)sin(pi/2-y)=-cos(x+y)

Let x and y be real numbers such that (sin x)/(sin y)=3 and (cos x)/(cos y)=(1)/(2). The value of (sin2x)/(sin2y)+(cos2x)/(cos2y) is (i)(49)/(58)(ii)(41)/(58)(iii)(51)/(58)( iv) none of these

Prove that: quad (cos x+cos y)^(2)+(sin x-sin y)^(2)=4cos^(2)(x+y)/(2)

Prove that: (cos x+cos y)^(2)+(sin x-sin y)^(2)=4cos^(2)backslash(x+y)/(2)

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

2(x-y sin2x)dx+(3y^(2)+cos2x)dy=0

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)