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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Add similar elements:

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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