What is the value of (tan(pi/4)+tan(pi/6))/(1-tan(pi/4)tan(pi/6)) ?

The value of (tan(pi/4)+tan(pi/6))/(1-tan(pi/4)tan(pi/6)) is 2+sqrt(3)

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(tan(pi/4)+tan(pi/6))/(1-tan(pi/4)tan(pi/6))

\frac{tan ( \frac{π}{4} ) + tan ( \frac{π}{6} )}{1 - tan ( \frac{π}{4} ) tan ( \frac{π}{6} )}

2 + 3

Solution steps

\frac{tan ( \frac{π}{4} ) + tan ( \frac{π}{6} )}{1 - tan ( \frac{π}{4} ) tan ( \frac{π}{6} )}

Use the following trivial identity:

tan (\frac{π}{4}) = 1

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

= \frac{1 + \frac{3}{3}}{1 - 1 \cdot \frac{3}{3}}

Simplify

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

= 2 + 3

arctan (\frac{13}{20})

sin (3 0^{\circ}) tan (4 5^{\circ}) + tan (3 0^{\circ}) sin (6 0^{\circ})

cos (arctan (- 3)) + csc (arcsec (2))

sin (\frac{π}{3} - arctan (\frac{1}{3}))

5 + 4 cos (\frac{π}{3})

What is the value of (tan(pi/4)+tan(pi/6))/(1-tan(pi/4)tan(pi/6)) ?
The value of (tan(pi/4)+tan(pi/6))/(1-tan(pi/4)tan(pi/6)) is 2+sqrt(3)