Question

Find the value of $\frac{8tan30^0}{1+ta{n}^{2}60^0}$.

• A. $cosec60^0$
• B. $cos60^0$
• C. $tan60^0$
• D. $sin60^0$

Answer 1

Answer: (A)

$cosec60^0$

We have, $\frac{8\tan {30}^0}{1+{\tan }^2{60}^0}$

$\Rightarrow \frac{8\times \frac{1}{\sqrt{3}}}{1+(\sqrt{3}{)}^2}$

$\Rightarrow \frac{\frac{8}{\sqrt{3}}}{1+3}$

$\Rightarrow \frac{\frac{8}{\sqrt{3}}}{4}$

$\Rightarrow \frac{2}{\sqrt{3}}$

$\Rightarrow cosec{60}^0$

Hence, this is the answer.