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[tex]2 \sin( \frac{5\pi}{6} ) - 4 \cos( \frac{2\pi}{3} ) + 6 \sin( \frac{3\pi}{4} ) - \cot( \frac{2\pi}{3} ) + \tan( \frac{5\pi}{6} ) [/tex]
2sin 5π/6-4cos 2π/3+6sin 3π/4-ctg 2π/3+tg 5π6
[tex]2 \sin( \frac{5\pi}{6} ) - 4 \cos( \frac{2\pi}{3} ) + 6 \sin( \frac{3\pi}{4} ) - \cot( \frac{2\pi}{3} ) + \tan( \frac{5\pi}{6} ) [/tex]
2sin 5π/6-4cos 2π/3+6sin 3π/4-ctg 2π/3+tg 5π6
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2sin 5π/6-4cos 2π/3+6sin 3π/4-ctg 2π/3+tg 5π6=
= 2*(1/2) -4*(- 1/2) +6*(√2/2) - ( - 1/√3) +(-1/√3) = 1+2+3√2 = 3+ 3√2