Question

$\frac{sin(-{660}^{\circ })tan\left({1050}^{\circ }\right)sec(-{420}^{\circ })}{cos\left({225}^{\circ }\right)cosec\left({315}^{\circ }\right)cos\left({510}^{\circ }\right)}=$

• A. $\sqrt{3}/4$
• B. $\sqrt{3}/2$
• C. $2/\sqrt{3}$
• D. $4/\sqrt{3}$

Answer 1

Answer: (C)

$2/\sqrt{3}$

$\frac{\sin (-660°)\tan \left(1050°\right)\sec (-420°)}{\cos \left(225°\right)cosec\left(315°\right)\cos \left(510°\right)}$

$=\frac{-\sin \left(660°\right)\tan \left(1050°\right)\sec (-420°)}{\cos \left(225°\right)cosec\left(315°\right)\cos \left(510°\right)}$

$=\frac{-\sin (4\times {180}^{\circ }-60°)\tan (6\times {180}^{\circ }-30°)\sec (2\times {180}^{\circ }+60°)}{\cos (\times {180}^{\circ }+45°)cosec(2\times {180}^{\circ }-45°)\cos (3\times {180}^{\circ }-30°)}$

$=\frac{-\sin (4\pi -60°)\tan (6\pi -30°)\sec (2\pi +60°)}{\cos (\pi +45°)cosec(2\pi -45°)\cos (3\pi -30°)}$

$=\frac{\sin 60°(-\tan 30°)\sec 60°}{-\cos 45°(-cosec45°)(-\cos 30°)}$

$=\frac{\frac{\sqrt{3}}{2}\times \left(\frac{-1}{\sqrt{3}}\right)\times 2}{\frac{1}{\sqrt{2}}\times -\sqrt{2}\times -\frac{\sqrt{3}}{2}}$

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

Hence, the answer is $\frac{2}{\sqrt{3}}.$