What is the value of 2sec^2(pi/6)tan(pi/6) ?

The value of 2sec^2(pi/6)tan(pi/6) is (8sqrt(3))/9

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2sec^2(pi/6)tan(pi/6)

2 sec^{2} (\frac{π}{6}) tan (\frac{π}{6})

\frac{8 3}{9}

Solution steps

2 sec^{2} (\frac{π}{6}) tan (\frac{π}{6})

Use the following trivial identity:

sec (\frac{π}{6}) = \frac{2 3}{3}

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

= 2 (\frac{2 3}{3})^{2} \frac{3}{3}

Simplify

2 (\frac{2 3}{3})^{2} \frac{3}{3} : \frac{8 3}{9}

= \frac{8 3}{9}

csc (\frac{7 π}{12})

2 cos (- π)

\frac{cos ( 3 0 ^{\circ} )}{cos ( 4 5 ^{\circ} )}

arctan (\frac{- 8}{6})

cos (3 0^{\circ}) + sin (4 5^{\circ})

What is the value of 2sec^2(pi/6)tan(pi/6) ?
The value of 2sec^2(pi/6)tan(pi/6) is (8sqrt(3))/9