Is cos(2x)-2cos^2(x)=-1 ?

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

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prove cos(2x)-2cos^2(x)=-1

prove

cos (2 x) - 2 cos^{2} (x) = - 1

True

Solution steps

cos (2 x) - 2 cos^{2} (x) = - 1

Manipulating left side

cos (2 x) - 2 cos^{2} (x)

Rewrite using trig identities

= - 1

We showed that the two sides could take the same form

\Rightarrow True

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

sin (x) tan (x) cos (x) = 1 - cos^{2} (x)

\frac{sin ( θ ) + sin ( 3 θ )}{2 sin ( 2 θ )} = cos (θ)

cos (2 A) = 1 - 2 sin^{2} (A)

cos (b) csc (b) tan (b) = 1