Trigonometry Examples

$2 \sin (x + 17) \cos (x + 17) = \cos (x + 8)$

Step 1

Simplify $2 \sin (x + 17) \cos (x + 17)$ .

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Step 1.1

Apply the sine double-angle identity.

$\sin (2 (x + 17)) = \cos (x + 8)$

Step 1.2

Simplify by multiplying through.

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Step 1.2.1

Apply the distributive property.

$\sin (2 x + 2 \cdot 17) = \cos (x + 8)$

Step 1.2.2

Multiply $2$ by $17$ .

$\sin (2 x + 34) = \cos (x + 8)$

Step 2

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

$x \approx 0.70353755 + 2 π n, 1.18436449 + 2 π n, 3.27875959 + 2 π n, 5.37315469 + 2 π n$ , for any integer $n$

Step 3