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

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

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

tan (\frac{7 π}{6} + \frac{7 π}{4})

3 - 2

Solution steps

tan (\frac{7 π}{6} + \frac{7 π}{4})

Rewrite using trig identities:

\frac{tan ( \frac{π}{6} ) + tan ( \frac{3 π}{4} )}{1 - tan ( \frac{π}{6} ) tan ( \frac{3 π}{4} )}

= \frac{tan ( \frac{π}{6} ) + tan ( \frac{3 π}{4} )}{1 - tan ( \frac{π}{6} ) tan ( \frac{3 π}{4} )}

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

Rewrite using trig identities:

tan (\frac{3 π}{4}) = - 1

= \frac{\frac{3}{3} - 1}{1 - \frac{3}{3} ( - 1 )}

Simplify

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

= 3 - 2

cos (\frac{4 π}{7}) cos (\frac{5 π}{21}) + sin (\frac{4 π}{7}) sin (\frac{5 π}{21})

arctan (cos (\frac{3 π}{2}))

9.8 \cdot cos (3 0^{\circ})

sin (arccos (0.6))

- sin^{2} (\frac{π}{4})

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