What is the value of ((tan(0)+1)-(tan(-pi/6)+1))/(0+pi/6) ?

The value of ((tan(0)+1)-(tan(-pi/6)+1))/(0+pi/6) is (2sqrt(3))/pi

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((tan(0)+1)-(tan(-pi/6)+1))/(0+pi/6)

\frac{( tan ( 0 ) + 1 ) - ( tan ( - \frac{π}{6} ) + 1 )}{0 + \frac{π}{6}}

\frac{2 3}{π}

Decimal Notation

1.10265 \dots

Solution steps

\frac{( tan ( 0 ) + 1 ) - ( tan ( - \frac{π}{6} ) + 1 )}{0 + \frac{π}{6}}

= \frac{tan ( 0 ) + 1 - ( tan ( - \frac{π}{6} ) + 1 )}{0 + \frac{π}{6}}

Use the following trivial identity:

tan (0) = 0

tan (0)

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 0

Rewrite using trig identities:

tan (- \frac{π}{6}) = - \frac{3}{3}

tan (- \frac{π}{6})

Use the following property:

tan (- x) = - tan (x)

tan (- \frac{π}{6}) = - tan (\frac{π}{6})

= - tan (\frac{π}{6})

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

tan (\frac{π}{6})

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

= - \frac{3}{3}

= \frac{0 + 1 - ( - \frac{3}{3} + 1 )}{0 + \frac{π}{6}}

Simplify

\frac{0 + 1 - ( - \frac{3}{3} + 1 )}{0 + \frac{π}{6}} : \frac{2 3}{π}

\frac{0 + 1 - ( - \frac{3}{3} + 1 )}{0 + \frac{π}{6}}

0 + \frac{π}{6} = \frac{π}{6}

= \frac{0 + 1 - ( - \frac{3}{3} + 1 )}{\frac{π}{6}}

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{( 0 + 1 - ( - \frac{3}{3} + 1 ) ) \cdot 6}{π}

Expand

0 + 1 - (- \frac{3}{3} + 1) : \frac{3}{3}

0 + 1 - (- \frac{3}{3} + 1)

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

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

Distribute parentheses

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

Apply minus-plus rules

- (- a) = a, - (a) = - a

= \frac{3}{3} - 1

= 0 + 1 + \frac{3}{3} - 1

0 + 1 - 1 = 0

= \frac{3}{3}

= \frac{6 \cdot \frac{3}{3}}{π}

Multiply

\frac{3}{3} \cdot 6 : 23

\frac{3}{3} \cdot 6

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 \cdot 6}{3}

Divide the numbers:

\frac{6}{3} = 2

= 23

= \frac{2 3}{π}

= \frac{2 3}{π}

sin^{2} (15 0^{\circ})

arctan (tan (\frac{11 π}{9}))

- 2 sin (\frac{3 π}{2})

sin (5)

- 4 cos (\frac{π}{3}) (1 + ln (7 sin (\frac{π}{3})))

What is the value of ((tan(0)+1)-(tan(-pi/6)+1))/(0+pi/6) ?
The value of ((tan(0)+1)-(tan(-pi/6)+1))/(0+pi/6) is (2sqrt(3))/pi