Is 2cos^2(θ)-1=1-2sin^2(θ) ?

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

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prove 2cos^2(θ)-1=1-2sin^2(θ)

prove

2 cos^{2} (θ) - 1 = 1 - 2 sin^{2} (θ)

True

Solution steps

2 cos^{2} (θ) - 1 = 1 - 2 sin^{2} (θ)

Manipulating left side

2 cos^{2} (θ) - 1

Rewrite using trig identities

= - 2 sin^{2} (θ) + 1

= 1 - 2 sin^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{1}{1 + sin ( x )} + \frac{1}{1 - sin ( x )} = 2 + 2 tan^{2} (x)

tan (a) = \frac{sin ( a )}{cos ( a )}

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

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

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