Simplify -cos(x)^4+sin(x)^4

$- \cos^{4} (x) + \sin^{4} (x)$

Step 1

Simplify the expression.

Rewrite $\sin^{4} (x)$ as ${(\sin^{2} (x))}^{2}$ .

$- \cos^{4} (x) + {(\sin^{2} (x))}^{2}$

Rewrite $\cos^{4} (x)$ as ${(\cos^{2} (x))}^{2}$ .

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

Reorder $- {(\cos^{2} (x))}^{2}$ and ${(\sin^{2} (x))}^{2}$ .

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

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \sin^{2} (x)$ and $b = \cos^{2} (x)$ .

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

Step 3

Apply pythagorean identity.

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

Step 4

Multiply $\sin^{2} (x) - \cos^{2} (x)$ by $1$ .

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

Simplify -cos(x)^4+sin(x)^4

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