What is the value of tan((7pi)/6+pi/4) ?

The value of tan((7pi)/6+pi/4) is 2+sqrt(3)

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tan((7pi)/6+pi/4)

tan (\frac{7 π}{6} + \frac{π}{4})

2 + 3

Solution steps

tan (\frac{7 π}{6} + \frac{π}{4})

Rewrite using trig identities:

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

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

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

Use the following trivial identity:

tan (\frac{π}{4}) = 1

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

Simplify

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

= 2 + 3

arcsin (\frac{6.1}{9.9})

25 cos (7 5^{\circ})

cos (arcsin (\frac{3}{5}) - arccos (\frac{1}{2}))

sec (\frac{11 π}{2})

arctan (\frac{9}{10})

What is the value of tan((7pi)/6+pi/4) ?
The value of tan((7pi)/6+pi/4) is 2+sqrt(3)