1. Вычислите \[ 1.1 \quad 2 \cdot\left(\operatorname{arctg}\left(-\frac{\sqrt{3}}{3}\right)+\arccos 0\right)-\operatorname{arcctg} \sqrt{3}: \]

simplifier les expressions suivantes : \( A=\cos 23^{\circ}+\cos ^{2} 75^{\circ}+\cos ^{2} 15^{\circ}-\sin 67^{\circ} \) \( B=\left(\sin ^{2} 65^{\circ}+\tan ^{2} 55^{\circ}+\sin ^{2} 25^{\circ}\right) \times \sin ^{2} 35^{\circ}-\tan 45^{\circ} \)

3. Решите неравенство \[ 2 \cos \left(2 x+\frac{\pi}{3}\right) \geq 1 \]

What is the definition of cosecant in relation to a right triangle?

(b) Express \( \left(\sqrt{3} \cos \theta+\sin \theta\right. \) in the form \( R \cos (\theta-\alpha) \), where \( R>0 \) and \( 0^{\circ}<\alpha<90^{\circ} \). Hence, solve the equation \( \sqrt{3} \cos \theta+\sin \theta=-1,0^{\circ}<\theta<360^{\circ} \).

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.