## Task B-4.1.

Solve the equation

$$
\sin x - \cos x + \tan x = 1
$$
First solution.

$$
\sin x-\cos x+\frac{\sin x}{\cos x}=1, \quad \cos x \neq 0
$$

Multiply the equation by $\cos x$ and we get

$$
\sin x \cdot \cos x-\cos ^{2} x+\sin x=\cos x
$$

By grouping the terms, we have

$$
\begin{aligned}
(\cos x+1) \cdot(\sin x-\cos x) & =0 \\
\cos x=-1 \quad \text { or } \quad \tan x & =1
\end{aligned}
$$

Then $x_{1}=\pi+2 k \pi, x_{2}=\frac{\pi}{4}+k \pi$.