Question

prove that cos3x=4cos3x-3cosx​

Answer 1

$\cos(3x)=\cos(2x+x)\\\\\cos(3x)=\cos(2x)\cos x-\sin(2x)\sin x\\\\\cos(3x)=(2\cos^2x-1)\cos x-2\sin^2x\cos x\\\\\cos(3x)=2\cos^3x-\cos x-2(1-\cos^2x)\cos x\\\\\cos(3x)=2\cos^3x-\cos x-2\cos x+2\cos^3x\\\\\boxed{\cos(3x)=4\cos^3x-3\cos x}$

Answer 2

See solution in image .....