Si se cumple que \( \tan ^{2} x=2+3 \tan ^{2} y \), calcule el valor de la siguiente expresión. \( \frac{1-\cos (x+y) \cos (x-y)}{\operatorname{sen}(x+y) \operatorname{sen}(x-y)-1} \)

2. a) Verify that \( \frac{\cos x}{1-\sin x}=\frac{1+\sin x}{\cos x} \) is true for \( x=\frac{\pi}{4} \). b) What are the non-permissible values for the equation?

A salvage vessel locates a sunken ship 168 m below the water's surface. It determines that the angle of depression to one end of the ship is \( 47.6^{\circ} \) and to the other end is \( 65.1^{\circ} \). Determine the length of the ship.

th Sketching the Graph of a Trigonometric Function hs In Exercises 15-38, sketch the graph of the function. (Include two full periods.) \( \begin{array}{ll}\text { 15. } y=\frac{1}{3} \tan x & \text { 16. } y=\tan 4 x \\ \text { 17. } y=-2 \tan 3 x & \text { 18. } y=-3 \tan \pi x \\ \text { 19. } y=-\frac{1}{2} \sec x & \text { 20. } y=\frac{1}{4} \sec x \\ \text { 21. } y=\csc \pi x & \text { 22. } y=3 \csc 4 x\end{array} \)

(iii) यदि \( \tan (\mathrm{A}+\mathrm{B})=\mathrm{p} \) तथा \( \tan (\mathrm{A}-\mathrm{B})=\mathrm{q} \) : तो \( \tan 2 \mathrm{~A} \) का मान ज्ञात कीजिए। \[ \text { If } \tan (\mathrm{A}+\mathrm{B})=\mathrm{p} \text { and } \tan (\mathrm{A}-\mathrm{B})=\mathrm{q} \text {; then find the value of } \tan 2 \mathrm{~A} \text {. } \]

The angle of elevation of the Sun is \( 33.1^{\circ} \) at the instant the shadow cast by a monument is 720 feet long. Use this information to calculate the height of the monument. The height of the monument is \( \square \mathrm{ft} \). (Round to two decimal places as needed.)