Trigonometry Examples

$\cos^{2} (40) - \sin^{2} (40) = \cos (A)$

Step 1

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

$\cos^{2} (40) - \sin^{2} (40) - \cos (A) = 0$

Step 2

Simplify $\cos^{2} (40) - \sin^{2} (40) - \cos (A)$ .

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Step 2.1

Apply the cosine double-angle identity.

$\cos (2 \cdot 40) - \cos (A) = 0$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $2$ by $40$ .

$\cos (80) - \cos (A) = 0$

Step 2.2.2

Evaluate $\cos (80)$ .

$0.17364817 - \cos (A) = 0$

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.