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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

= 1 - cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

tan^{4} (θ) - sec^{4} (θ) = 1 - 2 sec^{2} (θ)

\frac{( - sin ^{2} ( a ) + 1 )}{cos ( a )} = cos (a)

sec (x) - tan (x) = cos (x)

tan (2 x) - tan (x) = \frac{tan ( x )}{cos ( 2 x )}

\frac{cos ^{2} ( t )}{cot ( t )} = cos (t) sin (t)

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