Find the product. Leave the result in trigonometric form. (Enter your an \[ \left[\frac{1}{3}\left(\cos \left(140^{\circ}\right)+i \sin \left(140^{\circ}\right)\right)\right]\left[\frac{4}{5}\left(\cos \left(240^{\circ}\right)+i \sin \left(240^{\circ}\right)\right)\right] \]

(0.50) - Qual é a medida do lado oposto ngulo de \( 30^{\circ} \), em um triângulo, sabendo que utros dois lados medem 2 e \( \sqrt{3} \) ?

Solve the following equation for \( \beta \) over the interval \( [0,2 \pi) \), giving exact answers in radian units. If an equation has no solution, enter DNE. Multiple solutions should be entered as a comma-separated list. \( \tan ^{2}(\beta)-1=-2 \tan (\beta) \) \( \beta=\square \)

Exercice 3 \( A B C \) un triangle tel que : \( A C-\sqrt{52} \mathrm{~cm} ; B H=9 \mathrm{~cm} \) et \( H C=4 \mathrm{~cm} \) Hest le profete orthogonal de \( A \) sur \( (B C) \). 1) Calculer \( A H \) et \( A B \). 2) Montrer que \( A B C \) est un triangle rectangle en \( A \). 3) Calculer \( \cos A B C ; \sin A B C \) et \( \tan A B C \)

Prove that \( \begin{array}{ll}\text { (1) } \sin 4 x=4 \sin x \cos x-8 \sin ^{3} x \cos x & \text { (2) } \cos 4 x=8 \cos ^{4} x-8 \cos ^{2} x+1\end{array} \)

Prove the following identities: (1) \( \frac{\sin 2 \theta}{\cos \theta}-\sin \theta=\tan \theta \cos \theta \)