mplify the following expressions without using a calculator \( \frac{\sin 210^{\circ} \cos 300^{\circ} \tan 240^{\circ}}{\cos 120^{\circ} \tan 150^{\circ} \sin 330^{\circ}} \) \( [\sin (-\theta)+\cos (360-\theta)]\left[\cos (90-\theta)+\frac{\sin \theta}{\tan \theta}\right] \) If \( \tan x=m+\frac{1}{m}, 90^{\circ} \leq x \leq 270^{\circ} \) and \( m+\frac{1}{m^{2}}=1 \) Calculate the value of \( x \) without the use of a calculator.

\( \begin{array}{ll}\text { (i) } \sin \theta=\square & \text { (ii) } \cos (90-\theta)=\square \\ \text { (iii) } \tan (90-\theta)=\square & \text { (iv) } \tan \theta=\square\end{array} \)

20. Resolver la ecuación \( 2 \cos ^{2} \varepsilon-\cos \varepsilon-1=0 \)

Em um triângulo retângulo, se um dos ângulos agudos mede 30 graus e a hipotenusa mede 12 cm, calcule a medida do cateto oposto a esse ângulo usando o Teorema de Pitágoras.

19. Comprobar en lo general la siguiente identidad \( \operatorname{sen} A \cdot \tan A+\cos A \equiv \sec A \)

35. Calcular: \( F=2 * \sqrt{1-2 \cos \left(\frac{\pi}{3}\right)=\operatorname{sen}\left(\frac{\pi}{3}\right)} \) \( \begin{array}{llll}\text { A) } \frac{\sqrt{3}}{2} & \text { B) } \frac{1}{2} & \text { C) } \sqrt{3}+1 & \text { D) } 1-\sqrt{3}\end{array} \)