What is 3+tan(x-pi/3) ?

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

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simplify 3+tan(x-pi/3)

simplify

3 + tan (x - \frac{π}{3})

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

Solution steps

3 + tan (x - \frac{π}{3})

Rewrite using trig identities

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

Use the basic trigonometric identity:

sin (x) = \frac{1}{csc ( x )}

= \frac{- cos ( x ) \frac{3}{2} + \frac{1}{2} \cdot \frac{1}{c s c ( x )}}{cos ( x ) \frac{1}{2} + \frac{3}{2} \cdot \frac{1}{c s c ( x )}}

Simplify

\frac{- cos ( x ) \frac{3}{2} + \frac{1}{2} \cdot \frac{1}{c s c ( x )}}{cos ( x ) \frac{1}{2} + \frac{3}{2} \cdot \frac{1}{c s c ( x )}} : \frac{- 3 cos ( x ) csc ( x ) + 1}{cos ( x ) csc ( x ) + 3}

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

csc (x) cos (x) = cot (x)

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

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

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

\frac{x e ^{x}}{x sin ( x )}

t^{2} sin (- 2 t)

2 sin (3 x + \frac{π}{4}) - 1

sin (\frac{π}{6} + θ)

sin (arccos (10 x))

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