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

cos (- 1410 \circ)

\frac{cos ( 9 0 ^{\circ} ) + cos ( 0 )}{2 cos ( 5 0 ^{\circ} )}

cos (2 (\frac{2 π}{3}))

\frac{4}{cos ( 4 0 ^{\circ} )}

2.1 sin (3 7^{\circ})

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)