Question

$\frac{\tan \left(\frac{35\pi }{6}\right).\sin \left(\frac{11\pi }{3}\right).\sec \left(\frac{7\pi }{3}\right)}{\cot \left(\frac{5\pi }{4}\right).cosec\left(\frac{7\pi }{4}\right).\cos \left(\frac{17\pi }{6}\right)}=$

• A. $\sqrt{\frac{2}{3}}$
• B. $-\sqrt{\frac{2}{3}}$
• C. $\sqrt{\frac{3}{2}}$
• D. $\frac{\sqrt{3}}{2}$

Answer 1

The correct option is A $\sqrt{\frac{2}{3}}$

$\frac{\tan (6\pi -\frac{\pi }{6})\sin (4\pi -\frac{\pi }{3})\sec (2\pi +\frac{\pi }{3})}{\cot (\pi +\frac{\pi }{4})cosec(2\pi -\frac{\pi }{4})\cos (3\pi -\frac{\pi }{6})}=\frac{-\frac{1}{\sqrt{3}}.(-\frac{\sqrt{3}}{2}).2}{1.(-\sqrt{2})(-\frac{\sqrt{3}}{2})}=\sqrt{\frac{2}{3}}$