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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Simplify

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

Rewrite using trig identities

1 - 2 cos^{2} (x)

Use the Double Angle identity:

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

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

= - cos (2 x)

= - cos (2 x)

We showed that the two sides could take the same form

\Rightarrow True

sec^{2} (θ) - cos^{2} (θ) = tan (θ) sin (θ)

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

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

16 (\frac{1 - cos ( 2 θ )}{2}) = 8 - 8 cos (2 θ)

cot (θ) sin (θ) cos (θ) = cos^{2} (θ)

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