QUESTION 6 Simplify the following expressions without using a calculator. \( \begin{array}{l}6.1 \quad \frac{\sin 210^{\circ} \cos 300^{\circ} \tan 240^{\circ}}{\cos 120^{\circ} \tan 150^{\circ} \sin 330^{\circ}} \\ 6.2 \\ {[\sin (-\theta)+\cos (360-\theta)]\left[\cos (90-\theta)+\frac{\sin \theta}{\tan \theta}\right]} \\ 6.3 \text { If } \tan x=m+\frac{1}{m}, 90^{\circ} \leq x \leq 270^{\circ} \text { and } m^{2}+\frac{1}{m^{2}}=1 \\ \text { Calculate the value of } x \text { without the use of a calculator. }\end{array} \)

Si el seno de un ángulo es \( \frac{3}{5} \), ¿cuál es el valor de su cosecante?

\( \begin{array}{llll}\text { (B) } \frac{1}{\sqrt{2}} & \text { (B) } \sqrt{3} & \text { (C) } \frac{1}{\sqrt{3}} & \text { (D) } \sqrt{2}\end{array} \) यदि एक मीनार की ऊंचाई तथा छाया की लंबाई समान हो, तो सूर्य का उन्नयन कोण है \( \begin{array}{llll}\text { (अ) } 30^{\circ} & \text { (ब) } 60^{\circ} & \text { (स) } 45^{\circ} & \text { (द) } 15^{\circ}\end{array} \) If the height of a tower and length of its shadow are same, then the angle of elevati \( \begin{array}{llll}\text { (A) } 30^{\circ} & \text { (B) } 60^{\circ} & \text { (C) } 45^{\circ} & \text { (D) }\end{array} \)

In terms of the sides of a right triangle, how would you express \( \tan(\theta) \)?

(22) If ABC is a triangle in which : \( 5 \sin \mathrm{~A} \sin \mathrm{~B}=6 \sin \mathrm{~B} \sin \mathrm{C}=9 \sin \mathrm{C} \sin \mathrm{A} \), then \( \mathrm{m}(\angle \mathrm{C})= \) \( \begin{array}{llll}\text { (a) } 28 & \text { (b) } 32 & \text { (c) } 36 & \text { (d) } 42\end{array} \) (23) If ABC is a triangle in which \( \cdot 6 a=4 h=3 c \), then the measure of the smallest

Définissez la fonction tangente en termes des côtés d'un triangle rectangle.