(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। \[ \text { If } \tan (\mathrm{A}+\mathrm{B})=\mathrm{p} \text { and } \tan (\mathrm{A}-\mathrm{B})=\mathrm{q} \text {; then find the value of } \tan 2 \mathrm{~A} \text {. } \]

When the function \( f(x)= \) sin \( x \) is reflected across the \( y \)-axis, identify the coordinates of the reflected point of \( \left(\frac{\pi}{2}, 1\right) \) across the \( y \)-axis. (1 point) \( \left(\frac{-\pi}{2},-1\right) \) \( \left(\frac{-\pi}{2}, 1\right) \) \( \left(\frac{\pi}{2},-1\right) \) \( \left(\frac{\pi}{2}, 1\right) \)

Which of the following correctly describes the phase shift of the function \( f(x)=\cos \left(3 x-\frac{\pi}{2}\right) ?(1 \) point) \( -\frac{\pi}{6} \) \( \frac{\pi}{6} \) \( \frac{\pi}{2} \) \( \frac{3 \pi}{2} \)

Find the height of a tree if the angle of elevation to its topmost part changes from \( 25^{\circ} \) to \( 45^{\circ} \) as the observer moves 10 m closert to the base of the tree.

o 2. Даны комплексные числа \( z_{1}=1-i \sqrt{3} \) и \( z_{2}=-2 \mathrm{i} \). Найти: а) \( z_{1}^{5}, \sqrt[3]{z_{2}} ; \) выполнить действия в тригонометрической форме; результат заппсать в алгебраической форме, в показательной форме; б) изобразить на комплексной плоскости числа \( z_{2} \overline{z_{2}} \); указать на чертеже их модули и аргументы.

Rewrite the cosine function \( f(x)=-3 \cos \left(x-\frac{\pi}{8}\right)+2 \) as a translated sine function. \( \begin{array}{l}\text { (1 point) } \\ f(x)=-3 \sin \left(x+\frac{\pi}{4}\right)+2 \\ f(x)=-3 \sin \left(x+\frac{\pi}{24}\right)+2 \\ f(x)=-3 \sin \left(x+\frac{3 \pi}{8}\right)+2 \\ f(x)=-3 \sin \left(x-\frac{5 \pi}{8}\right)+2\end{array} \)