What is the value of (cos(pi/6))/(1-sin(pi/6)) ?

The value of (cos(pi/6))/(1-sin(pi/6)) is square root of 3

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(cos(pi/6))/(1-sin(pi/6))

\frac{cos ( \frac{π}{6} )}{1 - sin ( \frac{π}{6} )}

3

Solution steps

\frac{cos ( \frac{π}{6} )}{1 - sin ( \frac{π}{6} )}

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

= \frac{\frac{3}{2}}{1 - \frac{1}{2}}

Simplify

\frac{\frac{3}{2}}{1 - \frac{1}{2}} : 3

= 3

23 (cos (- \frac{5 π}{3}) + i sin (- \frac{5 π}{3}))

- cos (1 7^{\circ})

arctan (\frac{0.016}{0.025})

arccos^{2} (1)

51 tan (1 5^{\circ})

What is the value of (cos(pi/6))/(1-sin(pi/6)) ?
The value of (cos(pi/6))/(1-sin(pi/6)) is square root of 3