Is cos^2(8x)-sin^2(8x)=cos(16x) ?

The answer to whether cos^2(8x)-sin^2(8x)=cos(16x) is True

prove cos^2(8x)-sin^2(8x)=cos(16x)

prove

cos^{2} (8 x) - sin^{2} (8 x) = cos (16 x)

True

Solution steps

cos^{2} (8 x) - sin^{2} (8 x) = cos (16 x)

Manipulating left side

cos^{2} (8 x) - sin^{2} (8 x)

Rewrite using trig identities

cos^{2} (8 x) - sin^{2} (8 x)

Use the Double Angle identity:

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

= cos (2 \cdot 8 x)

Simplify

= cos (16 x)

= cos (16 x)

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (2 x) = \frac{1}{2} + \frac{1}{2} cos (4 x)

2 sin (- t) cos (- t) = 2 sin (- t) cos (t)

sin^{2} (α) + sin^{2} (α) tan^{2} (α) = tan^{2} (α)

cos (7 5^{\circ}) = \frac{1 + cos ( 15 0 ^{\circ} )}{2}

cos (7 x) - cos (3 x) = - 2 sin (5 x) sin (2 x)

Is cos^2(8x)-sin^2(8x)=cos(16x) ?
The answer to whether cos^2(8x)-sin^2(8x)=cos(16x) is True