Trigonometry Examples

sin (x) + sin (- x) - cos (- x)

$\sin (x) + \sin (- x) - \cos (- x)$

Step 1

Simplify each term.

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Step 1.1

Since

sin (- x)

$\sin (- x)$ is an odd function, rewrite

sin (- x)

$\sin (- x)$ as

- sin (x)

$- \sin (x)$ .

sin (x) - sin (x) - cos (- x)

$\sin (x) - \sin (x) - \cos (- x)$

Step 1.2

Since

cos (- x)

$\cos (- x)$ is an even function, rewrite

cos (- x)

$\cos (- x)$ as

cos (x)

$\cos (x)$ .

sin (x) - sin (x) - cos (x)

$\sin (x) - \sin (x) - \cos (x)$

sin (x) - sin (x) - cos (x)

$\sin (x) - \sin (x) - \cos (x)$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract

sin (x)

$\sin (x)$ from

sin (x)

$\sin (x)$ .

0 - cos (x)

$0 - \cos (x)$

Step 2.2

Subtract

cos (x)

$\cos (x)$ from

0

$0$ .

- cos (x)

$- \cos (x)$

- cos (x)

$- \cos (x)$

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

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