\( \begin{array}{ll}\text { IDENTIDADES TRIGONOMÉTRICAS } & \text { 8. }(\operatorname{sen} v+\cos v)^{2}+(\operatorname{sen} v-\cos v)^{2}=2 \\ \text { Demostrar las siguientes identidades } & \text { 9. }(\operatorname{sen} v+\operatorname{cosec} v)^{2}=\operatorname{sen}^{2} v+\operatorname{cotan}^{2} v+3 \\ \text { 1. } \cos v \tan v=\operatorname{sen} v & \text { 10. } \sec ^{2} v-\sec ^{2} v=\tan ^{4} v-\tan ^{2} v \\ \text { 2. } \cot v \cdot \tan v=1 & \text { 11. }(\sec v+\cos v)(\sec v-\cos v)=\tan ^{2} v+\operatorname{sen}^{2} v \\ \text { 3. } \operatorname{sen} v \cot v+\cos v \tan v=\operatorname{sen} v+\cos v & \text { 12. }\left(1+\tan ^{2} v\right) \cos ^{2} v=1 \\ \text { 4. } \operatorname{sen} v \sec v=\tan v & \text { 13. } \operatorname{sen}^{2} v+\operatorname{sen}^{2} v \tan ^{2} v=\tan ^{2} v\end{array} \)

A pylon \( \$ \$ 23.7 \$ \$ \mathrm{~m} \) high casts a shadow \( \$ \$ 46.8 \$ \$ \mathrm{~m} \) long. Determine the angle of elevation of the sun to the nearest tenth of a degree. 23.7 m high casts a shadow 46.8 m long. Determine the angle of elevation of the sun to the nearest tenth of a degree. Show answer

\( \operatorname { coti } x + \operatorname { cosec } x = 11 \)

\( \left(\sec 79.36^{\circ}\right)\left(\sin 79.36^{\circ}\right)-\left(\tan 79.36^{\circ}\right)=\underline{\text { Blank } 1} \)

i) \( \frac{\tan \theta \cot \theta}{\sec \theta} \) equals: A \( \sin \theta \)

(d) Quando fazemos determinaçōes experimentais de uma grandeza \( X \), representamos seu valor numérico final acompanhado do erro \( \Delta X \) associado à medida, na forma \( X \pm \Delta X \). Para calcularmos o valor de uma funçāo \( f(X \pm \Delta X) \), utilizamos a regra \[ f(X \pm \Delta X)=f(X) \pm f^{\prime}(X) \Delta X \] Obtenha as fórmulas referentes a (i) \( \sin (X \pm \Delta X) \) e (ii) \( \cos (X \pm \Delta X) \)