Trigonometry Examples

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

Step 1

Subtract $1$ from both sides of the equation.

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

Step 2

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

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Step 2.1

Move $- 1$ .

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

Step 2.2

Reorder $\cos^{2} (2 x)$ and $- 1$ .

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

Step 2.3

Rewrite $- 1$ as $- 1 (1)$ .

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

Step 2.4

Factor $- 1$ out of $\cos^{2} (2 x)$ .

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

Step 2.5

Factor $- 1$ out of $- 1 (1) - 1 (- \cos^{2} (2 x))$ .

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

Step 2.6

Rewrite $- 1 (1 - \cos^{2} (2 x))$ as $- (1 - \cos^{2} (2 x))$ .

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

Step 2.7

Apply pythagorean identity.

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

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.