Trigonometry Examples

$3 \sin (x) - \cos (2 x) + 1$

Step 1

Simplify each term.

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Step 1.1

Use the double-angle identity to transform $\cos (2 x)$ to $1 - 2 \sin^{2} (x)$ .

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Multiply $- 1$ by $1$ .

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

Step 1.4

Multiply $- 2$ by $- 1$ .

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

Step 2

Combine the opposite terms in $3 \sin (x) - 1 + 2 \sin^{2} (x) + 1$ .

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Step 2.1

Add $- 1$ and $1$ .

$3 \sin (x) + 0 + 2 \sin^{2} (x)$

Step 2.2

Add $3 \sin (x)$ and $0$ .

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

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