Вариант 6 1. Представить в тригонометрической и в показательной форме число \( z=-1-i \sqrt{3} \).

JSTION 11 Prove the following identity: \( \frac{\cos ^{2}\left(90^{\circ}+\theta\right)}{\cos (-\theta)+\sin \left(90^{\circ}-\theta\right) \cos \theta}=\frac{1}{\cos \theta}-1 \) Determine the general solution of: \( \tan x \sin x+\cos x \tan x=0 \). Consider the following expression: \( 2 \sin ^{2} 3 x-\sin ^{2} x-\cos ^{2} x \) 11.3.1 Simplify the expression to a single trigonometric ratio of \( x \). 11.3.2 Write down the maximum value of the expression.

The value of \( \sec \left(300^{\circ}\right) \sin \left(270^{\circ}-\theta\right)+\tan \left(-45^{\circ}\right) \cos \left(360^{\circ}-\theta\right) \) is \( \begin{array}{llll}\text { (a) }-3 \sin \theta & \text { (b) }-3 \cos \theta & \text { (c) } 3 \cos \theta & \text { (d) } 0\end{array} \)

(6) The value of \( \sec \left(300^{\circ}\right) \sin \left(270^{\circ}-\theta\right)+\tan \left(-45^{\circ}\right) \cos (3 M-9) \) is \( \begin{array}{lll}\text { (a) }-3 \sin \theta & \text { (b) }-3 \cos \theta & \text { (c) } 3 \cos \theta\end{array} \) (7) If the product of two roots of the equation : \( (k-2) x^{2}-6 x+12=0 \) equals 3

11) The measure of the smallest positive angle satisfy the relation : \( 2 \sin \theta=-1 \) is \( \begin{array}{lll}\text { (a) } 30^{\circ} & \text { (b) } 120^{\circ} & \text { (c) } 210^{\circ} y=x\end{array} \)

Exercice 1: D. Ecrirc sous forme trigonométrique : \( z_{1}=2\left(\cos \frac{\pi}{4}-i \sin \frac{\pi}{4}\right) \) \( \begin{array}{ll}z_{2}=-3\left(\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}\right) \quad z_{3}=2\left(\cos \frac{\pi}{4}+i \sin \frac{3 \pi}{4}\right) \\ z_{4}=\cos \frac{\pi}{6}+i \sin \left(-\frac{\pi}{6}\right) \quad z_{5}=\cos \theta-i \sin \theta \quad z_{5}=\sin \theta+i \cos \theta\end{array} \)