Trigonometry Examples

$\cos^{2} (8 x) - \sin^{2} (8 x) = \cos (B)$

Step 1

Subtract $\cos (B)$ from both sides of the equation.

$\cos^{2} (8 x) - \sin^{2} (8 x) - \cos (B) = 0$

Step 2

Simplify $\cos^{2} (8 x) - \sin^{2} (8 x) - \cos (B)$ .

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Step 2.1

Apply the cosine double-angle identity.

$\cos (2 (8 x)) - \cos (B) = 0$

Step 2.2

Multiply $8$ by $2$ .

$\cos (16 x) - \cos (B) = 0$

Step 3

Add $\cos (B)$ to both sides of the equation.

$\cos (16 x) = \cos (B)$

Step 4

For the two functions to be equal, the arguments of each must be equal.

$16 x = B$

Step 5

Divide each term in $16 x = B$ by $16$ and simplify.

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Step 5.1

Divide each term in $16 x = B$ by $16$ .

$\frac{16 x}{16} = \frac{B}{16}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $16$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{16 x}{16} = \frac{B}{16}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{B}{16}$