What is the value of (tan(60)+tan(45))/(1-tan(60)tan(45)) ?

The value of (tan(60)+tan(45))/(1-tan(60)tan(45)) is -2-sqrt(3)

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(tan(60)+tan(45))/(1-tan(60)tan(45))

\frac{tan ( 6 0 ^{\circ} ) + tan ( 4 5 ^{\circ} )}{1 - tan ( 6 0 ^{\circ} ) tan ( 4 5 ^{\circ} )}

- 2 - 3

Solution steps

\frac{tan ( 6 0 ^{\circ} ) + tan ( 4 5 ^{\circ} )}{1 - tan ( 6 0 ^{\circ} ) tan ( 4 5 ^{\circ} )}

Use the following trivial identity:

tan (6 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

arctan (- \frac{5}{6})

arccos (cos (1))

sin (arcsin (\frac{3}{2}) + arccos (1))

sin (11 6^{\circ})

2 cos (2 \cdot 0)

What is the value of (tan(60)+tan(45))/(1-tan(60)tan(45)) ?
The value of (tan(60)+tan(45))/(1-tan(60)tan(45)) is -2-sqrt(3)