What is the value of tan(pi/3-pi/4) ?

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

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tan(pi/3-pi/4)

tan (\frac{π}{3} - \frac{π}{4})

2 - 3

Solution steps

tan (\frac{π}{3} - \frac{π}{4})

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

ln (sec (\frac{π}{2}))

arccos (1.13178)

arcsec (\frac{7}{4})

0 + cos (0)

arctan (\frac{17}{12})