What is the value of (tan(30)+tan(15))/(1-tan(30)tan(15)) ?

The value of (tan(30)+tan(15))/(1-tan(30)tan(15)) is 1

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(tan(30)+tan(15))/(1-tan(30)tan(15))

\frac{tan ( 3 0 ^{\circ} ) + tan ( 1 5 ^{\circ} )}{1 - tan ( 3 0 ^{\circ} ) tan ( 1 5 ^{\circ} )}

1

Solution steps

\frac{tan ( 3 0 ^{\circ} ) + tan ( 1 5 ^{\circ} )}{1 - tan ( 3 0 ^{\circ} ) tan ( 1 5 ^{\circ} )}

Use the following trivial identity:

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

Rewrite using trig identities:

tan (1 5^{\circ}) = 2 - 3

= \frac{\frac{3}{3} + 2 - 3}{1 - \frac{3}{3} ( 2 - 3 )}

Simplify

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

= 1

cot (- \frac{3}{3})

6 cos (- \frac{2 π}{3})

40 cos (2 0^{\circ})

sin (\frac{19 π}{12}) - sin (\frac{π}{12})

csc (\frac{2}{3})

What is the value of (tan(30)+tan(15))/(1-tan(30)tan(15)) ?
The value of (tan(30)+tan(15))/(1-tan(30)tan(15)) is 1