Just write it as $\dfrac {\sin(30)}{\cos(30)} + \dfrac {\cos(30)}{\sin(30)}$ and simplify
9) Show that tan30 + 1/tan30 = 1/sin30cos30
So, for this I just subbed in the appropriate trig ratios and solved it to get 2.3, which is the same for both. However, the answer in the book has it as 4√3/3. I know this equals the same thing, but I'm not sure how to get it in that format...Could someone show and explain the steps? Thanks! (:
What Romsek says is I think the easiest way, but you could also evaluate each of the ratios directly...
$\displaystyle \begin{align*} LHS &= \tan{ \left( 30^{\circ} \right) } + \frac{1}{\tan{ \left( 30^{\circ} \right) } } \\ &= \frac{ 1}{\sqrt{3}} + \frac{1}{\frac{1}{\sqrt{3}}} \\ &= \frac{\sqrt{3}}{3} + \sqrt{3} \\ &= \frac{4\sqrt{3}}{3} \end{align*}$
while
$\displaystyle \begin{align*} RHS &= \frac{1}{\sin{ \left( 30^{\circ} \right) } \cos{ \left( 30^{\circ} \right) } } \\ &= \frac{1}{\frac{1}{2} \cdot \frac{\sqrt{3}}{2} } \\ &= \frac{1}{\frac{\sqrt{3}}{4}} \\ &= \frac{4}{\sqrt{3}} \\ &= \frac{4\sqrt{3}}{3} \\ &= LHS \end{align*}$