Is cos^2(θ)-sin^2(θ)=1-2sin^2(θ) ?

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

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prove cos^2(θ)-sin^2(θ)=1-2sin^2(θ)

prove

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

True

Solution steps

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

Manipulating left side

cos^{2} (θ) - sin^{2} (θ)

Rewrite using trig identities

cos^{2} (θ) - sin^{2} (θ)

Use the Pythagorean identity:

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

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

= 1 - sin^{2} (θ) - sin^{2} (θ)

Add similar elements:

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

= 1 - 2 sin^{2} (θ)

= 1 - 2 sin^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

tan^{5} (x) = tan^{3} (x) sec^{2} (x) - tan^{3} (x)

\frac{cos ( x )}{cot ( x )} = sin (x)

tan^{2} (x) (csc^{2} (x) - 1) = 1

cos (x) csc (x) = cot (x)

csc (x) = \frac{1}{sin ( x )}

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