What is the value of (tan(15)+tan(15))/(1-tan(15)tan(15)) ?

The value of (tan(15)+tan(15))/(1-tan(15)tan(15)) is (sqrt(3))/3

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(tan(15)+tan(15))/(1-tan(15)tan(15))

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

\frac{3}{3}

Solution steps

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

Simplify

= \frac{2 tan ( 1 5 ^{\circ} )}{1 - tan ^{2} ( 1 5 ^{\circ} )}

Rewrite using trig identities:

tan (3 0^{\circ})

= tan (3 0^{\circ})

Use the following trivial identity:

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

= \frac{3}{3}

arctan (\frac{- 2 3}{2})

cos (\frac{4}{7})

cos^{2} (31 5^{\circ})

sin (\frac{- 13 π}{12})

sin (\frac{3 π}{7})

What is the value of (tan(15)+tan(15))/(1-tan(15)tan(15)) ?
The value of (tan(15)+tan(15))/(1-tan(15)tan(15)) is (sqrt(3))/3