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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Add similar elements:

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

= 2 cos^{2} (x)

= 2 cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

- 2 sin (2 x + π) = - 2 sin (2 x - π)

cos (θ) (\frac{1}{1 - sin ( θ )}) = sec (θ) + tan (θ)

2 sin (a + b) sin (a - b) = cos (2 b) - cos (2 a)

\frac{1}{sin ( x )} = 2

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

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