2. Responde las siguientes preguntas. a. ¿Para qué casos se aplican la ley de senos y la ley del coseno? b. ¿Cómo se deduce la ley del coseno para un triángulo obtusángulo?

\( \left. \begin{array} { l } { ( t ) = \frac { \sin t } { \cos t } } \\ { \frac { 2 \cos ( 3 t ) \cos ( 2 t ) + 3 \sin ( 2 t ) \sin ( 3 t ) } { \cos ^ { 2 } ( 3 t ) } } \\ { \frac { 2 \cos ( 3 t ) \cos ( 2 t ) - 3 \sin ( 2 t ) \sin ( 3 t ) } { \cos ^ { 2 } ( 3 t ) } } \\ { \frac { \sin ^ { 2 } ( t ) + \cos ^ { 2 } ( t ) } { \cos ^ { 2 } ( t ) } } \\ { \frac { \cos ( t ) \cos ( t ) - \sin ( t ) \sin ( t ) } { \cos ( t ) } } \end{array} \right. \)

Buktikan \( \frac{1-\cos a}{\sin ^{2} a}=\frac{1}{1+\cos a} \)

Hallar " \( x \) ", si: \( \frac{\operatorname{Cos} 5 x+\operatorname{Cos} x}{\operatorname{Sen} 5 x+\operatorname{Sen} x}=1 \)

Use an identity to solve the following equation on the interval \( [0,2 \pi) \). \( 2 \sin ^{2} x-\cos x-1=0 \) Select the correct choice below and, if necessary, fill in the answer box to com A. \( x= \) (Type your answer in radians. Use integers or fractions for any numbe needed. Use a comma to separate answers as needed.) B. There is no solution.

8. (3 points) Evaluate \( \arctan (1)=\tan ^{-1}(1) \) \( \begin{array}{ll}\text { A } \frac{\pi}{3} & \text { (B) } \frac{\pi}{2} \\ \text { (C) } \frac{\pi}{4} & \text { (D) } \frac{\pi}{6}\end{array} \)