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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Add similar elements:

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

sin (24 0^{\circ})

cos (\frac{7 π}{3})

cos (\frac{17 π}{12})

sin^{2} (2 π)

arccot (3)

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