What is tan(x+pi/3) ?

The solution to tan(x+pi/3) is (1+sqrt(3)cot(x))/(cot(x)-sqrt(3))

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simplify tan(x+pi/3)

simplify

tan (x + \frac{π}{3})

\frac{1 + 3 cot ( x )}{cot ( x ) - 3}

Solution steps

tan (x + \frac{π}{3})

Rewrite using trig identities

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

Rewrite using trig identities

= \frac{1 + cot ( x ) 3}{cot ( x ) - 3}

cos (2 x) + cos (- 2 x)

sec (arctan (\frac{2}{x}))

tan (θ) 1 - sin^{2} (θ)

sin (t + 2 π) \cdot sec (t + 2 π)

\frac{2 csc ( 2 t )}{csc ( - t )}

What is tan(x+pi/3) ?
The solution to tan(x+pi/3) is (1+sqrt(3)cot(x))/(cot(x)-sqrt(3))