Trigonometry Examples

$\cos^{2} (\frac{π}{13}) - \sin^{2} (\frac{π}{13})$

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \cos (\frac{π}{13})$ and $b = \sin (\frac{π}{13})$ .

$(\cos (\frac{π}{13}) + \sin (\frac{π}{13})) (\cos (\frac{π}{13}) - \sin (\frac{π}{13}))$

Step 2

Simplify.

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Step 2.1

Evaluate $\cos (\frac{π}{13})$ .

$(0.97094181 + \sin (\frac{π}{13})) (\cos (\frac{π}{13}) - \sin (\frac{π}{13}))$

Step 2.2

Evaluate $\sin (\frac{π}{13})$ .

$(0.97094181 + 0.23931566) (\cos (\frac{π}{13}) - \sin (\frac{π}{13}))$

Step 2.3

Add $0.97094181$ and $0.23931566$ .

$1.21025748 (\cos (\frac{π}{13}) - \sin (\frac{π}{13}))$

Step 2.4

Evaluate $\cos (\frac{π}{13})$ .

$1.21025748 (0.97094181 - \sin (\frac{π}{13}))$

Step 2.5

Evaluate $\sin (\frac{π}{13})$ .

$1.21025748 (0.97094181 - 1 \cdot 0.23931566)$

Step 2.6

Multiply $- 1$ by $0.23931566$ .

$1.21025748 (0.97094181 - 0.23931566)$

Step 2.7

Subtract $0.23931566$ from $0.97094181$ .

$1.21025748 \cdot 0.73162615$