What is the value of (tan(60)-tan(30))/(1+tan(60)*tan(30)) ?

The value of (tan(60)-tan(30))/(1+tan(60)*tan(30)) is (sqrt(3))/3

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(tan(60)-tan(30))/(1+tan(60)*tan(30))

\frac{tan ( 6 0 ^{\circ} ) - tan ( 3 0 ^{\circ} )}{1 + tan ( 6 0 ^{\circ} ) \cdot tan ( 3 0 ^{\circ} )}

\frac{3}{3}

Solution steps

\frac{tan ( 6 0 ^{\circ} ) - tan ( 3 0 ^{\circ} )}{1 + tan ( 6 0 ^{\circ} ) tan ( 3 0 ^{\circ} )}

Use the following trivial identity:

tan (6 0^{\circ}) = 3

Use the following trivial identity:

tan (3 0^{\circ}) = \frac{3}{3}

= \frac{3 - \frac{3}{3}}{1 + 3 \frac{3}{3}}

Simplify

\frac{3 - \frac{3}{3}}{1 + 3 \frac{3}{3}} : \frac{3}{3}

= \frac{3}{3}

arctan (1.333)

sin (- \frac{3}{4})

cos (1 5^{\circ}) cos (1 5^{\circ}) - sin (1 5^{\circ}) sin (1 5^{\circ})

sin (\frac{1}{2} arctan (- \frac{5}{13}))

tan (- 0.01)

What is the value of (tan(60)-tan(30))/(1+tan(60)*tan(30)) ?
The value of (tan(60)-tan(30))/(1+tan(60)*tan(30)) is (sqrt(3))/3