### Home > PC3 > Chapter 11 > Lesson 11.2.2 > Problem11-106

11-106.

Solve: $\sin4(x) – \cos4(x) =\frac { 1 } { 2 }$

Factor.

Substitute using the Fundamental Pythagorean Identity.

Substitute using the Fundamental Pythagorean Identity, rewritten.

Combine like terms and subtract $1$ from both sides.

Divide both sides by $−2$.

Square root both sides. Don't forget the $±$.

$\text{Sketch a unit circle to find all angles whose cosine is }\pm \frac{1}{2}.$

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

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

$1-\cos^2(x)-\cos^2(x)=\frac{1}{2}$

$-2\cos^2(x)=-\frac{1}{2}$

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

$\cos(x)=\pm \frac{1}{2}$