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Trigonometry Examples

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

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

Step 1

Simplify each term.

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Step 1.1

Use the double-angle identity to transform

cos (2 x)

$\cos (2 x)$ to

1 - 2 {sin}^{2} (x)

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

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

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

Step 1.2

Apply the distributive property.

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

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

Step 1.3

Multiply

- 1

$- 1$ by

1

$1$ .

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

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

Step 1.4

Multiply

- 2

$- 2$ by

- 1

$- 1$ .

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

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

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

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

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Step 2.1

Add

- 1

$- 1$ and

1

$1$ .

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

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

Step 2.2

Add

3 sin (x)

$3 \sin (x)$ and

0

$0$ .

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

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

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

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

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⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$