---
title: DeclareMathOperator
tags: math
---

$$
\DeclareMathOperator{\tg}{tg}
\DeclareMathOperator{\ctg}{ctg}
$$

$$
\cos\alpha = 0.8
$$

$$
\cos\alpha = \frac{4}{5}
$$

---

$$
\sin^2\alpha + \cos^2\alpha = 1
$$

$$
\sin^2\alpha = 1 - \cos^2\alpha
$$

$$
\sin\alpha = \sqrt{1 - \cos^2\alpha}
$$

$$
\sin\alpha = \sqrt{1 - (\frac{4}{5})^2}
$$

$$
\sin\alpha = \sqrt{1 - \frac{16}{25}}
$$

$$
\sin\alpha = \sqrt{\frac{9}{25}}
$$

$$
\sin\alpha = \sqrt{(\frac{3}{5})^2}
$$

$$
\sin\alpha = \frac{3}{5}
$$

---

$$
\tg\alpha = \frac{\sin\alpha}{\cos\alpha}
$$

$$
\tg\alpha = \frac{\frac{3}{5}}{\frac{4}{5}}
$$

$$
\tg\alpha = \frac{3}{5} \cdot \frac{5}{4}
$$

$$
\tg\alpha = \frac{15}{20}
$$

$$
\tg\alpha = \frac{3}{4}
$$

---

$$
2\sin\alpha + 3\tg^2\alpha = 2 \cdot \frac{3}{5} + 3 \cdot (\frac{3}{4})^2 = \frac{6}{5} + 3 \cdot \frac{9}{16} = \frac{6}{5} + \frac{27}{16} = 1.2 + 1.6875 = 2.8875
$$

---

$$
\frac{x - 2}{x + 2} = x - 2
$$

$$
x - 2 = (x - 2)(x + 2)
$$

$$
x - 2 = x^2 - 4
$$

$$
x^2 - x - 2 = 0
$$

Licz deltę!

---

$$
-6-x = \frac{12+4x}{2}
$$

$$
-12-2x = 12+4x
$$

$$
-24 = 6x
$$

$$
x = -4
$$