What is the general solution for tan(1/2 x)=0 ?

The general solution for tan(1/2 x)=0 is x=2pin

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tan(1/2 x)=0

tan (\frac{1}{2} x) = 0

x = 2 πn

Degrees

x = 0^{\circ} + 36 0^{\circ} n

Solution steps

tan (\frac{1}{2} x) = 0

General solutions for

tan (\frac{1}{2} x) = 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}

\frac{1}{2} x = 0 + πn

\frac{1}{2} x = 0 + πn

Solve

\frac{1}{2} x = 0 + πn : x = 2 πn

\frac{1}{2} x = 0 + πn

0 + πn = πn

\frac{1}{2} x = πn

Multiply both sides by

2

\frac{1}{2} x = πn

Multiply both sides by

2

2 \cdot \frac{1}{2} x = 2 πn

Simplify

x = 2 πn

x = 2 πn

x = 2 πn

2 cos (x) = - 2, 0 \leq x < 2 π

3 sec (x) csc (x) = 2 csc (x)

(2 sin (x) - 1) (2 cos (x) - 3) = 0

cos (θ) = - \frac{6}{7}

sec (θ) = - 5

What is the general solution for tan(1/2 x)=0 ?
The general solution for tan(1/2 x)=0 is x=2pin