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(sin(-4pi/3))(cos(11pi/6))-(tan(5pi/6))(cos(pi/3))

 Mar 21, 2019
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(sin(-4pi/3))(cos(11pi/6))-(tan(5pi/6))(cos(pi/3))

 

\(sin(\frac{-4\pi}{3})(cos(\frac{11\pi}{6})- tan(\frac{5\pi}{6})(cos\frac{\pi}{3})\\ =sin(2\pi+\frac{-4\pi}{3})(cos(2\pi-\frac{11\pi}{6}))- tan(\frac{5\pi}{6})(cos\frac{\pi}{3})\\ =sin(\frac{2\pi}{3})(cos(\frac{\pi}{6}))- tan(\frac{5\pi}{6})(cos\frac{\pi}{3})\\ =sin(\frac{\pi}{3})(cos(\frac{\pi}{6}))-- tan(\frac{\pi}{6})(cos\frac{\pi}{3})\\ =\frac{\sqrt3}{2}\times\frac{\sqrt3}{2}+ \frac{1}{\sqrt3}\times \frac{1}{2}\\ =\frac{3}{4}+ \frac{1}{2\sqrt3}\times \frac{\sqrt3}{\sqrt3}\\ =\frac{3}{4}+ \frac{\sqrt3}{6}\\ =\frac{9}{12}+ \frac{2\sqrt3}{12}\\ = \frac{9+2\sqrt3}{12}\\ \)

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 Mar 21, 2019

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