Trigonometry Examples

$3 \sin^{2} (x) + 4 \cos^{2} (x) = 3 + \cos^{2} (x)$

Step 1

Start on the left side.

$3 \sin^{2} (x) + 4 \cos^{2} (x)$

Step 2

Apply Pythagorean identity in reverse.

$3 (1 - \cos^{2} (x)) + 4 \cos^{2} (x)$

Step 3

Simplify.

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$3 \cdot 1 + 3 (- {\cos (x)}^{2}) + 4 {\cos (x)}^{2}$

Step 3.1.2

Multiply $3$ by $1$ .

$3 + 3 (- {\cos (x)}^{2}) + 4 {\cos (x)}^{2}$

Step 3.1.3

Multiply $- 1$ by $3$ .

$3 - 3 {\cos (x)}^{2} + 4 {\cos (x)}^{2}$

Step 3.2

Add $- 3 {\cos (x)}^{2}$ and $4 {\cos (x)}^{2}$ .

$3 + \cos^{2} (x)$

Step 4

Because the two sides have been shown to be equivalent, the equation is an identity.

$3 \sin^{2} (x) + 4 \cos^{2} (x) = 3 + \cos^{2} (x)$ is an identity