Is cos(x)-1=(cos(2x)-1)/(2(cos(x)+1)) ?

The answer to whether cos(x)-1=(cos(2x)-1)/(2(cos(x)+1)) is True

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prove cos(x)-1=(cos(2x)-1)/(2(cos(x)+1))

prove

cos (x) - 1 = \frac{cos ( 2 x ) - 1}{2 ( cos ( x ) + 1 )}

True

Solution steps

cos (x) - 1 = \frac{cos ( 2 x ) - 1}{2 ( cos ( x ) + 1 )}

Manipulating right side

\frac{cos ( 2 x ) - 1}{2 ( cos ( x ) + 1 )}

Rewrite using trig identities

= cos (x) - 1

We showed that the two sides could take the same form

\Rightarrow True

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Is cos(x)-1=(cos(2x)-1)/(2(cos(x)+1)) ?
The answer to whether cos(x)-1=(cos(2x)-1)/(2(cos(x)+1)) is True