Question

The second part of the problem is where i need help. The answers i have there have been given by other tutors

Answer 1

SOLUTION

From the given value

Since

$\sin u=\frac{7}{25}$

Then using trigonometrical ratios it follows

$\cos u=\frac{24}{25}$

Using hal -ngle it folows

$\begin{gathered} sin(\frac{u}{2})=\sqrt{\frac{1-\frac{24}{25}}{2}} \\ s\imaginaryI n(\frac{u}{2})=\sqrt{\frac{1}{50}} \end{gathered}$

Also

$\begin{gathered} cos(\frac{u}{2})=\pm\sqrt{\frac{1+\frac{24}{25}}{2}} \\ cos(\frac{u}{2})=\sqrt{\frac{49}{50}} \\ cos(\frac{u}{2})=7\sqrt{\frac{1}{50}} \end{gathered}$

Finally?

$\begin{gathered} \tan(\frac{u}{2})=\pm\sqrt{\frac{1-\frac{24}{25}}{1+\frac{24}{25}}} \\ \tan(\frac{u}{2})=\sqrt{\frac{1}{49}} \\ \tan(\frac{u}{2})=\frac{1}{7} \end{gathered}$