What is the value of tan((11pi)/6-(5pi)/4) ?

The value of tan((11pi)/6-(5pi)/4) is -2-sqrt(3)

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tan((11pi)/6-(5pi)/4)

tan (\frac{11 π}{6} - \frac{5 π}{4})

- 2 - 3

Solution steps

tan (\frac{11 π}{6} - \frac{5 π}{4})

Simplify:

\frac{11 π}{6} - \frac{5 π}{4} = \frac{7 π}{12}

= tan (\frac{7 π}{12})

Rewrite using trig identities:

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

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

Use the following trivial identity:

tan (\frac{π}{3}) = 3

Use the following trivial identity:

tan (\frac{π}{4}) = 1

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

Simplify

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

= - 2 - 3

8 \cdot sin (5 0^{\circ})

2 sin (5 0^{\circ})

2 sin (2 5^{\circ}) cos (2 5^{\circ})

arcsin (- 7)

sin (3 0^{\circ}) cos (1 5^{\circ}) + cos (3 0^{\circ}) sin (1 5^{\circ})

What is the value of tan((11pi)/6-(5pi)/4) ?
The value of tan((11pi)/6-(5pi)/4) is -2-sqrt(3)