\( (\operatorname{sen} \alpha+\cos \alpha)^{2}=1+\frac{2 \operatorname{sen} \alpha}{\cos \alpha} \) 5. \( \quad \operatorname{tg} \alpha \cdot \cot \alpha=\operatorname{sen}^{2} \alpha+\cos ^{2} \alpha \) 6. \( \quad \operatorname{tg} \alpha+\cot \alpha=\sec \alpha \cdot \operatorname{cosec} \alpha \) 7. \( \operatorname{sen} \alpha \cdot \sec \alpha=\operatorname{tg} \alpha \) 8. \( \quad \operatorname{sen} \alpha \cdot \cos \alpha \) \( \frac{\cos ^{2} \alpha-\operatorname{sen}^{2} \alpha}{\operatorname{tg}}=\frac{\operatorname{tg} \alpha}{1-\operatorname{tg}^{2} \alpha} \)

4) \( \operatorname{Si} \tan \Phi=\frac{\sqrt{6}}{3} \), donde " \( \Phi \) " es un ángulo agudo, calcular: \( \mathrm{P}=\sqrt{3} \operatorname{Sec} \Phi+\sqrt{2} \operatorname{Csc} \Phi \)

Solve \( \sin ^{2}(t)=-8 \cos (t) \) for all solutions \( 0 \leq t<2 \pi \)

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

6 A plane flies on a true bearing of \( 280^{\circ} \mathrm{T} \) at \( 600 \mathrm{~km} / \mathrm{h} \) after taking off at 1300 hours. To the nearest kilometre, how far north of its starting position is it at 1530 hours?

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