What is 1-tan(x+pi/3) ?

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

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simplify 1-tan(x+pi/3)

simplify

1 - tan (x + \frac{π}{3})

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

Solution steps

1 - tan (x + \frac{π}{3})

Rewrite using trig identities

= 1 - \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)

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

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

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

4 sin (x - \frac{π}{2})

\frac{r}{tan ( 5 4 ^{\circ} )}

- cos (π + x)

sin (πn) - sin (- πn)

sin (0 + x)

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