What is the value of (tan(120)+tan(45))/(1-tan(120)tan(45)) ?

The value of (tan(120)+tan(45))/(1-tan(120)tan(45)) is -2+sqrt(3)

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(tan(120)+tan(45))/(1-tan(120)tan(45))

\frac{tan ( 12 0 ^{\circ} ) + tan ( 4 5 ^{\circ} )}{1 - tan ( 12 0 ^{\circ} ) tan ( 4 5 ^{\circ} )}

- 2 + 3

Solution steps

\frac{tan ( 12 0 ^{\circ} ) + tan ( 4 5 ^{\circ} )}{1 - tan ( 12 0 ^{\circ} ) tan ( 4 5 ^{\circ} )}

Rewrite using trig identities:

tan (12 0^{\circ}) = - 3

Use the following trivial identity:

tan (4 5^{\circ}) = 1

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

Simplify

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

= - 2 + 3

tan (2) + tan (1)

\frac{5}{cos ( 9 0 ^{\circ} )}

2 - 2 cos (\frac{π}{4})

2 sin (3 7^{\circ})

2 cot (π)

What is the value of (tan(120)+tan(45))/(1-tan(120)tan(45)) ?
The value of (tan(120)+tan(45))/(1-tan(120)tan(45)) is -2+sqrt(3)