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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 + tan ( θ )}{1 + cot ( θ )} = tan (θ)

cos (x + 1) = cos (- x - 1)

cos (x) (tan (x) sec (x)) = sin (x) - 1

\frac{tan ( θ )}{sin ( θ )} = sec (θ)

tan (u) - sec (u) = \frac{cos ( u )}{1 + sin ( u )}

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