Algebra Examples

$2 u = 14 °$ , $\cos (2 u) = \cos^{2} (u) - \sin^{2} (u)$

Step 1

Divide each term in $2 u = 14 °$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 u = 14 °$ by $2$ .

$\frac{2 u}{2} = \frac{14 °}{2}$

$\cos (2 u) = \cos^{2} (u) - \sin^{2} (u)$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 u}{2} = \frac{14 °}{2}$

$\cos (2 u) = \cos^{2} (u) - \sin^{2} (u)$

Step 1.2.1.2

Divide $u$ by $1$ .

$u = \frac{14 °}{2}$

$\cos (2 u) = \cos^{2} (u) - \sin^{2} (u)$

$u = \frac{14 °}{2}$

$\cos (2 u) = \cos^{2} (u) - \sin^{2} (u)$

$u = \frac{14 °}{2}$

$\cos (2 u) = \cos^{2} (u) - \sin^{2} (u)$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $14 °$ by $2$ .

$u = 7$

$\cos (2 u) = \cos^{2} (u) - \sin^{2} (u)$

$u = 7$

$\cos (2 u) = \cos^{2} (u) - \sin^{2} (u)$

$u = 7$

$\cos (2 u) = \cos^{2} (u) - \sin^{2} (u)$

Step 2

Replace all occurrences of $u$ with $7$ in each equation.

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Step 2.1

Replace all occurrences of $u$ in $\cos (2 u) = \cos^{2} (u) - \sin^{2} (u)$ with $7$ .

$\cos (2 (7)) = \cos^{2} (7) - \sin^{2} (7)$

$u = 7$

Step 2.2

Simplify $\cos (2 (7)) = \cos^{2} (7) - \sin^{2} (7)$ .

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Simplify $\cos (2 (7))$ .

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Step 2.2.1.1.1

Multiply $2$ by $7$ .

$\cos (14) = \cos^{2} (7) - \sin^{2} (7)$

$u = 7$

Step 2.2.1.1.2

Evaluate $\cos (14)$ .

$0.97029572 = \cos^{2} (7) - \sin^{2} (7)$

$u = 7$

$0.97029572 = \cos^{2} (7) - \sin^{2} (7)$

$u = 7$

$0.97029572 = \cos^{2} (7) - \sin^{2} (7)$

$u = 7$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Simplify $\cos^{2} (7) - \sin^{2} (7)$ .

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Step 2.2.2.1.1

Apply the cosine double-angle identity.

$0.97029572 = \cos (2 \cdot 7)$

$u = 7$

Step 2.2.2.1.2

Multiply $2$ by $7$ .

$0.97029572 = \cos (14)$

$u = 7$

Step 2.2.2.1.3

Evaluate $\cos (14)$ .

$0.97029572 = 0.97029572$

$u = 7$

$0.97029572 = 0.97029572$

$u = 7$

$0.97029572 = 0.97029572$

$u = 7$

$0.97029572 = 0.97029572$

$u = 7$

$0.97029572 = 0.97029572$

$u = 7$

Step 3

Remove any equations from the system that are always true.

$u = 7$