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

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

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

tan (\frac{7 π}{6} - \frac{π}{4})

3 - 2

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} : 3 - 2

= 3 - 2

cos (\frac{45}{2})

cot (2 4^{\circ})

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

arctan (- 3.51)

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

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