$a)\sqrt{3}cos^2x+\sin 2x-\sqrt{3}\sin^2x=1$$b)\cos 7x\cos 5-\sqrt{3}\sin 2x=1-\sin 7x\sin 5x$$c)4(\sin^4x+\cos^4x)+\sqrt{3}\sin 4x=2$$d)2\sin 4x=\sin x+\sqrt{3}\cos x$$e)\sin x+\sin 2x=\sqrt{3}(\cos x+\cos 2x)$$f)\cos^3x+\sin x-3\sin^2x\cos x=0$$g)2\sin^2(x-\pi/4)=2\sin^2x-\tan x$$f)1+\sin^3x+\cos^3x=\frac{3}{2}\sin 2x$$i)\sin^23x-\cos^24x=\sin^25x-\cos^26x$$k)5\cos x-2\sin\frac{x}{2}=-3$$l)2\sin 4x+16\sin^3x\cos x+3\cos 2x=5$$m)\sin^2x(\tan x+1)=3\sin x(\cos x-\sin x)+3$