Trigonometry Examples

$\sin (180 - x) = \frac{1 - (\cos^{2} (x))}{\sin (x)}$

Step 1

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

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Step 1.1

Apply pythagorean identity.

$\sin (180 - x) = \frac{\sin^{2} (x)}{\sin (x)}$

Step 1.2

Cancel the common factor of $\sin^{2} (x)$ and $\sin (x)$ .

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Step 1.2.1

Factor $\sin (x)$ out of $\sin^{2} (x)$ .

$\sin (180 - x) = \frac{\sin (x) \sin (x)}{\sin (x)}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Multiply by $1$ .

$\sin (180 - x) = \frac{\sin (x) \sin (x)}{\sin (x) \cdot 1}$

Step 1.2.2.2

Cancel the common factor.

$\sin (180 - x) = \frac{\sin (x) \sin (x)}{\sin (x) \cdot 1}$

Step 1.2.2.3

Rewrite the expression.

$\sin (180 - x) = \frac{\sin (x)}{1}$

Step 1.2.2.4

Divide $\sin (x)$ by $1$ .

$\sin (180 - x) = \sin (x)$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 2.03540569 + π n$ , for any integer $n$

Step 3