Is sin^2(θ)-cos^2(θ)=1-2cos^2(θ) ?

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

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prove sin^2(θ)-cos^2(θ)=1-2cos^2(θ)

prove

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

True

Solution steps

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

Manipulating left side

sin^{2} (θ) - cos^{2} (θ)

Rewrite using trig identities

sin^{2} (θ) - cos^{2} (θ)

Use the Pythagorean identity:

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

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

= 1 - cos^{2} (θ) - cos^{2} (θ)

Add similar elements:

- cos^{2} (θ) - cos^{2} (θ) = - 2 cos^{2} (θ)

= 1 - 2 cos^{2} (θ)

= 1 - 2 cos^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

sin (t) csc (t) = 1

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

cos (x) = sin (x + \frac{π}{2})

sec (2 θ) = \frac{sec ^{2} ( θ )}{2 - sec ^{2} ( θ )}

\frac{cot ( x )}{tan ( x ) + cot ( x )} = cos^{2} (x)

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