Question 17
Let $a$, $b$, $c$ be real numbers and let $a \neq 0$. Prove that at least one of the equations
$$
a \sin x + b \cos x + c = 0,
$$
$$
a \operatorname{tgg} y + b \operatorname{ctg} y + 2c = 0
$$
has real solutions.
$$
a \sin x + b \cos x + c = 0,
$$
$$
a \operatorname{tgg} y + b \operatorname{ctg} y + 2c = 0
$$
has real solutions.