Trigonometry Examples

$1 - \cos (7 x) \cos (x) - \sin (7 x) \sin (x) = 2 \sin^{2} (3 x)$

Step 1

Subtract $2 \sin^{2} (3 x)$ from both sides of the equation.

$1 - \cos (7 x) \cos (x) - \sin (7 x) \sin (x) - 2 \sin^{2} (3 x) = 0$

Step 2

Simplify $1 - \cos (7 x) \cos (x) - \sin (7 x) \sin (x) - 2 \sin^{2} (3 x)$ .

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Step 2.1

Move $- 2 \sin^{2} (3 x)$ .

$1 - 2 \sin^{2} (3 x) - \cos (7 x) \cos (x) - \sin (7 x) \sin (x) = 0$

Step 2.2

Apply the cosine double-angle identity.

$\cos (2 (3 x)) - \cos (7 x) \cos (x) - \sin (7 x) \sin (x) = 0$

Step 2.3

Multiply $3$ by $2$ .

$\cos (6 x) - \cos (7 x) \cos (x) - \sin (7 x) \sin (x) = 0$

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.