What is the general solution for cot^2(x)=(tan(x))/2 ?

The general solution for cot^2(x)=(tan(x))/2 is x=0.89990…+pin

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cot^2(x)=(tan(x))/2

cot^{2} (x) = \frac{tan ( x )}{2}

x = 0.89990 \dots + πn

Solution steps

cot^{2} (x) = \frac{tan ( x )}{2}

Subtract

\frac{tan ( x )}{2}

from both sides

cot^{2} (x) - \frac{tan ( x )}{2} = 0

Simplify

cot^{2} (x) - \frac{tan ( x )}{2} : \frac{2 cot ^{2} ( x ) - tan ( x )}{2}

\frac{2 cot ^{2} ( x ) - tan ( x )}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

2 cot^{2} (x) - tan (x) = 0

Rewrite using trig identities

- \frac{1}{cot ( x )} + 2 cot^{2} (x) = 0

Solve by substitution

cot (x) = - \frac{2 ^{\frac{2}{3}}}{4} + i \frac{2 ^{\frac{2}{3}} 3}{4} :

No Solution

cot (x) = - \frac{2 ^{\frac{2}{3}}}{4} - i \frac{2 ^{\frac{2}{3}} 3}{4} :

No Solution

Combine all the solutions

Show solutions in decimal form

x = 0.89990 \dots + πn

tan (θ) = \frac{3.2}{4.1}

5 sec (x) tan (x) = 0

cos (5 x) - cos (x) = 2 sin (2 x)

6 arccos (4 x) = 5 π

2 sin^{2} (x) - cos (x) = 1, 0 \leq x \leq 2 π

What is the general solution for cot^2(x)=(tan(x))/2 ?
The general solution for cot^2(x)=(tan(x))/2 is x=0.89990…+pin