Question

Find the value of
sin(-660°).cos(405°).cot(600°)/
sec(570°).cosec(330°).tan(480°). ?

Answer 1

$$\begin{gathered} \frac{\sin \left(-660\right)\times \cos 405\times \cot 600}{\sec 570\times \mathrm{cosec}330\times \tan 480} \\ =\frac{-\sin 660\times \cos 405\times \cot 600}{\sec 570\times \mathrm{cosec}330\times \tan 480} \\ =\frac{-\sin \left(630+30\right)\times \cos \left(360+45\right)\times \cot \left(630-60\right)}{\sec \left(540+30\right)\times \mathrm{cosec}\left(360-30\right)\times \tan \left(450+30\right)} \\ =\frac{-\left(-\cos 30\right)\times \cos 45\times \tan 60}{\sec 30\times \left(-\mathrm{cosec}30\right)\times \left(-\cot 30\right)} \\ =\frac{\cos 30\times \cos 45\times \tan 60}{\sec 30\times \mathrm{cosec}30\times \cot 30} \\ =\frac{{\displaystyle \frac{\sqrt{3}}{2}}\times {\displaystyle \frac{1}{\sqrt{2}}}\times \sqrt{3}}{{\displaystyle \frac{2}{\sqrt{3}}}\times 2\times \sqrt{3}} \\ =\frac{3}{8\sqrt{2}} \\ =\frac{3\sqrt{2}}{16} \end{gathered}$$