What is the general solution for 3cot(x)+1=2+4cot(x),0<= x<= 360 ?

The general solution for 3cot(x)+1=2+4cot(x),0<= x<= 360 is x=135,x=315

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3cot(x)+1=2+4cot(x),0<= x<= 360

3 cot (x) + 1 = 2 + 4 cot (x), 0^{\circ} \leq x \leq 36 0^{\circ}

x = 13 5^{\circ}, x = 31 5^{\circ}

Solution steps

3 cot (x) + 1 = 2 + 4 cot (x), 0^{\circ} \leq x \leq 36 0^{\circ}

Solve by substitution

cot (x) = - 1

cot (x) = - 1, 0 \leq x \leq 36 0^{\circ} : x = 13 5^{\circ}, x = 31 5^{\circ}

Combine all the solutions

x = 13 5^{\circ}, x = 31 5^{\circ}

sin (x) = \frac{48.35}{50.14}

2 tan (\frac{π x}{2}) = sec (\frac{π x}{2})

1.47 = (\frac{sin ( \frac{x + 60}{2} )}{sin ( 3 0 ^{\circ} )})

sin^{2} (x) + 1 = 3 sin (x) - 1

2 tan (θ) = sec^{2} (θ)

What is the general solution for 3cot(x)+1=2+4cot(x),0<= x<= 360 ?
The general solution for 3cot(x)+1=2+4cot(x),0<= x<= 360 is x=135,x=315