What is the general solution for tan(x/2)=\pm sqrt((1-cos(x))/(1+cos(x))) ?

The general solution for tan(x/2)=\pm sqrt((1-cos(x))/(1+cos(x))) is No Solution for x\in\mathbb{R}

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tan(x/2)=\pm sqrt((1-cos(x))/(1+cos(x)))

tan (\frac{x}{2}) = \pm \frac{1 - cos ( x )}{1 + cos ( x )}

No Solution for x \in R

Solution steps

tan (\frac{x}{2}) = \pm \frac{1 - cos ( x )}{1 + cos ( x )}

Subtract

\pm \frac{1 - cos ( x )}{1 + cos ( x )}

from both sides

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

General solutions for

tan (\frac{x}{2}) = 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{x}{2} = 0 + πn

\frac{x}{2} = 0 + πn

Solve

\frac{x}{2} = 0 + πn : x = 2 πn

\frac{x}{2} = 0 + πn

0 + πn = πn

\frac{x}{2} = πn

Multiply both sides by

2

\frac{x}{2} = πn

Multiply both sides by

2

\frac{2 x}{2} = 2 πn

Simplify

x = 2 πn

x = 2 πn

x = 2 πn

Since the equation is undefined for:

2 πn

No Solution for x \in R

sin^{2} (x) - cos^{2} (x) = 0.5

sec (x) - tan (x) = 1

7 cos^{2} (θ) + 6 cos (θ) - 12 = 7 cos (θ) - 6

sin^{2} (x) = sin (x) + 1 - sin^{2} (x)

tan^{2} (x) - 3 sec (x) + 3 = 0

What is the general solution for tan(x/2)=\pm sqrt((1-cos(x))/(1+cos(x))) ?
The general solution for tan(x/2)=\pm sqrt((1-cos(x))/(1+cos(x))) is No Solution for x\in\mathbb{R}