What is the general solution for (15-sqrt(3))/3 =5-2/3*csc(4x+pi/2) ?

The general solution for (15-sqrt(3))/3 =5-2/3*csc(4x+pi/2) is No Solution for x\in\mathbb{R}

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(15-sqrt(3))/3 =5-2/3*csc(4x+pi/2)

\frac{15 - 3}{3} = 5 - \frac{2}{3} \cdot csc (4 x + \frac{π}{2})

No Solution for x \in R

Solution steps

\frac{15 - 3}{3} = 5 - \frac{2}{3} csc (4 x + \frac{π}{2})

Switch sides

5 - \frac{2}{3} csc (4 x + \frac{π}{2}) = \frac{15 - 3}{3}

Move

5

to the right side

5 - \frac{2}{3} csc (4 x + \frac{π}{2}) = \frac{15 - 3}{3}

Subtract

5

from both sides

5 - \frac{2}{3} csc (4 x + \frac{π}{2}) - 5 = \frac{15 - 3}{3} - 5

Simplify

- \frac{2}{3} csc (4 x + \frac{π}{2}) = \frac{15 - 3}{3} - 5

- \frac{2}{3} csc (4 x + \frac{π}{2}) = \frac{15 - 3}{3} - 5

Multiply both sides by

3

- \frac{2}{3} csc (4 x + \frac{π}{2}) = \frac{15 - 3}{3} - 5

Multiply both sides by

3

3 (- \frac{2}{3} csc (4 x + \frac{π}{2})) = 3 \cdot \frac{15 - 3}{3} - 3 \cdot 5

Simplify

3 (- \frac{2}{3} csc (4 x + \frac{π}{2})) = 3 \cdot \frac{15 - 3}{3} - 3 \cdot 5

Simplify

3 (- \frac{2}{3} csc (4 x + \frac{π}{2})) : - 2 csc (4 x + \frac{π}{2})

3 (- \frac{2}{3} csc (4 x + \frac{π}{2}))

Remove parentheses:

(- a) = - a

= - 3 \cdot \frac{2}{3} csc (4 x + \frac{π}{2})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{2 \cdot 3}{3} csc (4 x + \frac{π}{2})

Cancel the common factor:

3

= - csc (4 x + \frac{π}{2}) \cdot 2

Simplify

3 \cdot \frac{15 - 3}{3} - 3 \cdot 5 : - 3

3 \cdot \frac{15 - 3}{3} - 3 \cdot 5

3 \cdot \frac{15 - 3}{3} = 15 - 3

3 \cdot \frac{15 - 3}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( 15 - 3 ) \cdot 3}{3}

Cancel the common factor:

3

= 15 - 3

3 \cdot 5 = 15

3 \cdot 5

Multiply the numbers:

3 \cdot 5 = 15

= 15

= 15 - 3 - 15

15 - 15 = 0

= - 3

- 2 csc (4 x + \frac{π}{2}) = - 3

- 2 csc (4 x + \frac{π}{2}) = - 3

- 2 csc (4 x + \frac{π}{2}) = - 3

Divide both sides by

- 2

- 2 csc (4 x + \frac{π}{2}) = - 3

Divide both sides by

- 2

\frac{- 2 csc ( 4 x + \frac{π}{2} )}{- 2} = \frac{- 3}{- 2}

Simplify

csc (4 x + \frac{π}{2}) = \frac{3}{2}

csc (4 x + \frac{π}{2}) = \frac{3}{2}

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

No Solution for x \in R

tan (x) + 4 sin (x) = 0

1 + 2 \cdot sin (x) = 2

1 + 2 \cdot sin (x) = 3

sin (α) = \frac{120 sin ( 6 0 ^{\circ} )}{1200}

15.8 \cdot sin (30 x - 90) + 5 = 17

What is the general solution for (15-sqrt(3))/3 =5-2/3*csc(4x+pi/2) ?
The general solution for (15-sqrt(3))/3 =5-2/3*csc(4x+pi/2) is No Solution for x\in\mathbb{R}