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

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

Popular >

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

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

- sin^{2} (θ) = cos^{2} (θ) - 1

sec (x) + cos (x) = tan (x) sin (x)

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

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