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

Solución

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

Sin soluci \overset{o}{ˊ} n para x \in R

Pasos de solución

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

Intercambiar lados

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

Mover

5

al lado derecho

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

Restar

5

de ambos lados

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

Simplificar

- \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

Multiplicar ambos lados por

3

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

Multiplicar ambos lados por

3

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

Simplificar

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

Simplificar

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}))

Quitar los parentesis:

(- a) = - a

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

Multiplicar fracciones:

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

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

Eliminar los terminos comunes:

3

= - csc (4 x + \frac{π}{2}) \cdot 2

Simplificar

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}

Multiplicar fracciones:

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

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

Eliminar los terminos comunes:

3

= 15 - 3

3 \cdot 5 = 15

3 \cdot 5

Multiplicar los numeros:

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

Dividir ambos lados entre

- 2

- 2 csc (4 x + \frac{π}{2}) = - 3

Dividir ambos lados entre

- 2

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

Simplificar

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

Sin soluci \overset{o}{ˊ} n para 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