What is the value of 2cos(pi/6)+sin(2(pi/6)) ?

The value of 2cos(pi/6)+sin(2(pi/6)) is sqrt(3)+(sqrt(3))/2

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2cos(pi/6)+sin(2(pi/6))

2 cos (\frac{π}{6}) + sin (2 (\frac{π}{6}))

3 + \frac{3}{2}

Solution steps

2 cos (\frac{π}{6}) + sin (2 (\frac{π}{6}))

= 2 cos (\frac{π}{6}) + sin (2 \cdot \frac{π}{6})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Rewrite using trig identities:

sin (2 \cdot \frac{π}{6}) = \frac{3}{2}

= 2 \cdot \frac{3}{2} + \frac{3}{2}

Simplify

2 \cdot \frac{3}{2} + \frac{3}{2} : 3 + \frac{3}{2}

= 3 + \frac{3}{2}

300 cos (4 5^{\circ})

60 sin (6 0^{\circ})

cos (\frac{3 π}{4} - \frac{π}{6})

cos (π - \frac{π}{4})

- csc (\frac{π}{3})

What is the value of 2cos(pi/6)+sin(2(pi/6)) ?
The value of 2cos(pi/6)+sin(2(pi/6)) is sqrt(3)+(sqrt(3))/2