Решите уравнение \( \operatorname{tg} \frac{\pi x}{4}=-1 \). В ответе напишите наибольший отрицательный корень.

Toždestwony subut edin: a) \( 1+2 \cos 2 \alpha+\cos 4 \alpha=4 \cos ^{2} \alpha \cos 2 \alpha \)

а) \( \operatorname{tg} \frac{\alpha}{2}=\frac{1-\cos \alpha}{\sin \alpha} \);

6.3 If \( \quad \tan x=m+\frac{1}{m}, 90^{\circ} \leq x \leq 270^{\circ} \) and \( m^{2}+\frac{1}{m^{2}}=1 \) Calculate the value of \( x \) without the use of a calculator.

3) \( \frac{\operatorname{tg}^{2} \alpha}{1+\operatorname{tg}^{2} \alpha}= \)

In a right triangle where one angle measures 30 degrees, how do you express the secant of that angle?