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

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

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

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

1

Solution steps

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

Rewrite using trig identities:

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

Use the following trivial identity:

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

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

Simplify

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

= 1

π - \frac{1}{2} sin (2 π)

arctan (\frac{34}{54})

cos (0.8 π)

sin (3) (\frac{π}{3})

tan (arccos (- \frac{3}{7}))

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