Trigonometry Examples

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

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

Step 1

Subtract

\cos (B)

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

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

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

Step 2

Simplify

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

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

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Step 2.1

Apply the cosine double-angle identity.

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

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

Step 2.2

Multiply

8

$8$ by

2

$2$ .

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

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

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

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

Step 3

Add

\cos (B)

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

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

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

Step 4

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

16 x = B

$16 x = B$

Step 5

Divide each term in

16 x = B

$16 x = B$ by

16

$16$ and simplify.

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Step 5.1

Divide each term in

16 x = B

$16 x = B$ by

16

$16$ .

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

$16$ .

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Step 5.2.1.1

Cancel the common factor.

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

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

Step 5.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{B}{16}

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

x = \frac{B}{16}

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

x = \frac{B}{16}

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

x = \frac{B}{16}

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

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$