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

The general solution for 3cot(3/2)+2csc(x/2)=0,0<= ,x<= 360 is No Solution for x\in\mathbb{R}

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3cot(3/2)+2csc(x/2)=0,0<= ,x<= 360

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

No Solution for x \in R

Solution steps

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

Move

3 cot (\frac{3}{2})

to the right side

3 cot (\frac{3}{2}) + 2 csc (\frac{x}{2}) = 0

Subtract

3 cot (\frac{3}{2})

from both sides

3 cot (\frac{3}{2}) + 2 csc (\frac{x}{2}) - 3 cot (\frac{3}{2}) = 0 - 3 cot (\frac{3}{2})

Simplify

2 csc (\frac{x}{2}) = - 3 cot (\frac{3}{2})

2 csc (\frac{x}{2}) = - 3 cot (\frac{3}{2})

Divide both sides by

2

2 csc (\frac{x}{2}) = - 3 cot (\frac{3}{2})

Divide both sides by

2

\frac{2 csc ( \frac{x}{2} )}{2} = \frac{- 3 cot ( \frac{3}{2} )}{2}

Simplify

csc (\frac{x}{2}) = - \frac{3 cot ( \frac{3}{2} )}{2}

csc (\frac{x}{2}) = - \frac{3 cot ( \frac{3}{2} )}{2}

csc (x) \leq - 1 or csc (x) \geq 1

No Solution for x \in R

What is the general solution for 3cot(3/2)+2csc(x/2)=0,0<= ,x<= 360 ?
The general solution for 3cot(3/2)+2csc(x/2)=0,0<= ,x<= 360 is No Solution for x\in\mathbb{R}