What is the value of tan(45+30) ?

The value of tan(45+30) is 2+sqrt(3)

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tan(45+30)

tan (4 5^{\circ} + 3 0^{\circ})

2 + 3

Solution steps

tan (4 5^{\circ} + 3 0^{\circ})

Rewrite using trig identities:

\frac{tan ( 4 5 ^{\circ} ) + tan ( 3 0 ^{\circ} )}{1 - tan ( 4 5 ^{\circ} ) tan ( 3 0 ^{\circ} )}

= \frac{tan ( 4 5 ^{\circ} ) + tan ( 3 0 ^{\circ} )}{1 - tan ( 4 5 ^{\circ} ) tan ( 3 0 ^{\circ} )}

Use the following trivial identity:

tan (4 5^{\circ}) = 1

Use the following trivial identity:

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

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

Simplify

\frac{1 + \frac{3}{3}}{1 - 1 \cdot \frac{3}{3}} : 2 + 3

= 2 + 3

tan (9 1^{\circ})

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

ln (cos (\frac{π}{2}))

4 (cos (\frac{π}{2}) + i sin (\frac{π}{2}))

\frac{10}{cos ( 3 0 ^{\circ} )}