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

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

p ro v e sin^{2} (x) = \frac{sec ( x ) sin ( x )}{tan ( x ) + cot ( x )}

p ro v e cot (A) = \frac{cos ( A )}{sin ( A )}

p ro v e 1 - 2 cos^{2} (4) = 2 sin^{2} (4) - 1

p ro v e sin (8 a) = 4 sin (2 a) cos (2 a) cos (4 a)

p ro v e csc^{2} (x) (tan (x)) - (tan (x)) = cot (x)

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