Is cos(2x)cos(x)-sin(2x)sin(x)=4cos^3(x)-3cos(x) ?

The answer to whether cos(2x)cos(x)-sin(2x)sin(x)=4cos^3(x)-3cos(x) is True

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prove cos(2x)cos(x)-sin(2x)sin(x)=4cos^3(x)-3cos(x)

prove

cos (2 x) cos (x) - sin (2 x) sin (x) = 4 cos^{3} (x) - 3 cos (x)

True

Solution steps

cos (2 x) cos (x) - sin (2 x) sin (x) = 4 cos^{3} (x) - 3 cos (x)

Manipulating left side

cos (2 x) cos (x) - sin (2 x) sin (x)

Rewrite using trig identities

= 4 cos^{3} (x) - 3 cos (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{( cot ( x ) + tan ( x ) )}{csc ( x )} = sec (x)

csc^{2} (b) - csc^{2} (b) cos^{2} (b) = 1

cos (\frac{5 θ}{2}) cos (\frac{θ}{2}) = \frac{1}{4} cos^{2} (5 θ)

sin (3 v) = 3 sin (v) - 4 sin^{3} (v)

2 sin (x + \frac{π}{4}) = sin (x) + cos (x)

Is cos(2x)cos(x)-sin(2x)sin(x)=4cos^3(x)-3cos(x) ?
The answer to whether cos(2x)cos(x)-sin(2x)sin(x)=4cos^3(x)-3cos(x) is True