Trigonometry Questions & Answers

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

14. \( \tan v+\operatorname{cotan} v=\sec v \operatorname{cosec} v \) 15. \( \operatorname{sen}^{2} v \cos ^{2} v+\cos ^{4} v=\cos ^{2} v \)

\( \begin{aligned} \text { a) } \quad \sin x & =0 \\ 0 & \leqslant x \\ 0 & \leqslant x \\ 0 & \leqslant 360^{\circ}\end{aligned} \)

5. \( \operatorname{sen} v \operatorname{cotan} v=\cos v \) 6. \( \operatorname{sen} v \tan v+\cos v=\sec v \) 7. \( \operatorname{csec} v-\operatorname{sen} v=\operatorname{cotan} v \cos v \) 8. \( (\operatorname{sen} v+\cos v)^{2}+(\operatorname{sen} v-\cos v)^{2}=2 \) 9. \( (\operatorname{sen} v+\operatorname{cosec} v)^{2}=\operatorname{sen}^{2} v+\operatorname{cotan}^{2} v+3 \) 10. \( \sec ^{4} v-\sec ^{2} v=\tan ^{4} v-\tan ^{2} v \) 11. \( \left(\sec ^{2} v+\cos ^{2} v\right)\left(\sec v-\cos ^{2} v\right)=\tan ^{2} v+\operatorname{sen}^{2} v \) 12. \( \left(1+\tan ^{2} v\right) \cos ^{2} v=1 \)

Sin utilizar tablas ni calculadora, calcula y simplifica: a) \( 3 \operatorname{sen} 30^{\circ}+6 \cos 45^{\circ} \) b) \( \operatorname{sen}^{2} 45^{\circ}+\cos ^{2} 45^{\circ} \) c) \( \tan ^{2} 60^{\circ}-\sec ^{2} 60^{\circ} \) d) \( \frac{\cos 60^{\circ}+\cos 30^{\circ}}{\csc ^{2} 30^{\circ}+\operatorname{sen}^{2} 45^{\circ}} \)

Sin utilizar tablas ni calculadora, calcula y simplifica: a) \( 3 \operatorname{sen} 30^{\circ}+6 \cos 45^{\circ} \) b) \( \operatorname{sen}^{2} 45^{\circ}+\cos ^{2} 45^{\circ} \) c) \( \tan ^{2} 60^{\circ}-\sec ^{2} 60^{\circ} \) d) \( \frac{\cos 60^{\circ}+\cos 30^{\circ}}{\csc ^{2} 30^{\circ}+\operatorname{sen}^{2} 45^{\circ}} \)

IDENTIDADES TRIGONOMÉTRICAS Demostrar las siguientes identidades 1. \( \cos \vee \tan v=\operatorname{sen} \downarrow \) 2. \( \cot \downarrow \cdot \tan v=1 \) 3. \( \operatorname{sen} \downarrow \cot v+\cos v \tan v=\operatorname{sen} v+\cos v \)

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

Use the sum or difference formula for tangent to find the exact value for \( \tan \left(-165^{\circ}\right) \) \( \tan \left(-165^{\circ}\right)=\square \)

Simplify and write the trigonometric expression in terms of sine and cosine: \( \frac{2+\tan ^{2} x}{\sec ^{2} x}-1=g(x) \) \( g(x)= \)