Trigonometry Examples

$\sin^{2} (x) = 9 (\cos (- x) - 1)$

Step 1

Subtract $9 (\cos (- x) - 1)$ from both sides of the equation.

$\sin^{2} (x) - 9 (\cos (- x) - 1) = 0$

Step 2

Simplify each term.

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Step 2.1

Since $\cos (- x)$ is an even function, rewrite $\cos (- x)$ as $\cos (x)$ .

$\sin^{2} (x) - 9 (\cos (x) - 1) = 0$

Step 2.2

Apply the distributive property.

$\sin^{2} (x) - 9 \cos (x) - 9 \cdot - 1 = 0$

Step 2.3

Multiply $- 9$ by $- 1$ .

$\sin^{2} (x) - 9 \cos (x) + 9 = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.