Is sin^2(x)-2cos^2(x)=1-3cos^2(x) ?

The answer to whether sin^2(x)-2cos^2(x)=1-3cos^2(x) is True

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prove sin^2(x)-2cos^2(x)=1-3cos^2(x)

prove

sin^{2} (x) - 2 cos^{2} (x) = 1 - 3 cos^{2} (x)

True

Solution steps

sin^{2} (x) - 2 cos^{2} (x) = 1 - 3 cos^{2} (x)

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Add similar elements:

- cos^{2} (x) - 2 cos^{2} (x) = - 3 cos^{2} (x)

= 1 - 3 cos^{2} (x)

= 1 - 3 cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

Is sin^2(x)-2cos^2(x)=1-3cos^2(x) ?
The answer to whether sin^2(x)-2cos^2(x)=1-3cos^2(x) is True