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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Rewrite using trig identities

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

Add similar elements:

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

sin (4 0^{\circ}) = 2 \cdot sin (2 0^{\circ}) \cdot cos (2 0^{\circ})

9 sec (y) cos (y) = 9

- sin (- x) = sin (x)

tan^{2} (x) + 2 = sec^{2} (x) + 1

csc (x) + sec (x) = tan (x)

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