Question

If Sin=1/3 , find the value of 9cot^2 +cot

Answer 1

solution

$cos = \sqrt{1 - ( \frac{1}{3} ) {}^{2} } = \frac{ \sqrt{8} }{3}$

therefore..

$= cot = \frac{cos}{sin} = \frac{ \frac{ \sqrt{8} }{3} }{ \frac{1}{3} } = \sqrt{8}$

$= 9cot {}^{2} + cot \\ = 9( \sqrt{8} ) {}^{2} + \sqrt{8} \\ = 9 \times 8 + \sqrt{8} \\ = 72 + 2 \sqrt{2} \\ = 36(2 + \sqrt{2} )$