\( \begin{array}{l}2.1 \text { If } \hat{\mathrm{A}}=310^{\circ} \text { and } \hat{\mathrm{B}}=130,5^{\circ} \text {, determine the following values, correct to ONE } \\ \text { decimal digit: } \\ 2.1 .1 \quad \tan 3 B+\frac{1}{3} \cos \frac{A}{3} \\ 2.1 .2 \quad-\sec \left(\frac{A}{4}-2 B\right) \\ 2.2 \text { If } \cot \theta=-\frac{12}{5} \text { and } \sin \theta>0 \text {, determine the value of } 20 \operatorname{cosec} \theta-12 \sec \theta \text {, } \\ \text { WITHOUT the use of a calculator. } \\ 2.3 \text { Simplify the following expression: } \\ 2.4 \text { Prove that: } \frac{1}{\tan \left(360^{\circ}-x\right) \sec \left(180^{\circ}+x\right) \operatorname{cosec}\left(360^{\circ}+x\right)} \\ 1+\cot ^{2} x\end{array} \frac{1}{1+\tan ^{2} x}=1 \)

1. Най иите а) \( -9 \cos \alpha ; \) б) \( \sqrt{2} \) tga, если \( \sin \alpha=-\frac{2 \sqrt{2}}{3} \quad \alpha \in\left(\frac{3 \pi}{2} ; 2 \pi\right) \)

Para determinar la altura de un edificio, Carlos se ubica a 10 metros del edificio y mide el ángulo de \( 40^{\circ} \). Si la altura de Carlos es de 1.47 metros, determine la altura del edificio.

value of: \( \frac{\sin \theta+\cos \theta}{2 \sin \theta} \) without using a calculator. \( 4.2 .1 \tan \left(-32^{\circ}\right) \) \( 4.2 .2 \sin 412^{\circ} \) Simplify the following fully and without using a calculator: \( \frac{\sin 120^{\circ} \cdot \tan 300^{\circ}}{\cos \left(-60^{\circ}\right) \cdot \tan 225^{\circ}} \) Prove the following identity: \( \frac{\cos 2 x-\cos x-\sin x}{2 \sin x \cos x+\sin x}=\frac{1}{\tan x}-\frac{1}{\sin x} \) Determine the general solution of: \( \sin (5 \theta)=\cos \left(\theta-40^{\circ}\right) \)

Al reducir la expresión CscaTanaCosa-Csc \( 2 a ~ a ~ u n a ~ s o l a ~ f u n c i o ́ n ~ t r i g o n o m e ́ t r i c a ~ s e ~ o b t i e n e: ~ \) \( 2 \operatorname{sen}^{2} a \) \( -\sec ^{2} a \) \( -\cot ^{2} a \)

Calcula la amplitud, el periodo y traza las gráficas: 7) \( y=\operatorname{sen}\left(\frac{x}{2}\right) \)