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

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

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

tan (\frac{7 π}{6} - \frac{7 π}{4})

2 + 3

Solution steps

tan (\frac{7 π}{6} - \frac{7 π}{4})

Simplify:

\frac{7 π}{6} - \frac{7 π}{4} = - \frac{7 π}{12}

= tan (- \frac{7 π}{12})

Use the following property:

tan (- x) = - tan (x)

tan (- \frac{7 π}{12}) = - tan (\frac{7 π}{12})

= - tan (\frac{7 π}{12})

Rewrite using trig identities:

tan (\frac{7 π}{12}) = - 2 - 3

= - (- 2 - 3)

Simplify

= 2 + 3

arctan (\frac{3}{5})

arcsin (csc (\frac{π}{2}))

cos (\frac{4 π}{7})

121 sin (4 5^{\circ})

sin (e^{- 1})

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