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4cot(x)=sqrt(3)csc(x)

Solución

4 cot (x) = 3 csc (x)

Solución

x = 1.12296 \dots + 2 πn, x = 2 π - 1.12296 \dots + 2 πn

+1

Grados

x = 64.34109 \dots^{\circ} + 36 0^{\circ} n, x = 295.65890 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

4 cot (x) = 3 csc (x)

Restar

3 csc (x)

de ambos lados

4 cot (x) - 3 csc (x) = 0

Expresar con seno, coseno

4 cot (x) - csc (x) 3

Utilizar la identidad trigonométrica básica:

cot (x) = \frac{cos ( x )}{sin ( x )}

= 4 \cdot \frac{cos ( x )}{sin ( x )} - csc (x) 3

Utilizar la identidad trigonométrica básica:

csc (x) = \frac{1}{sin ( x )}

= 4 \cdot \frac{cos ( x )}{sin ( x )} - \frac{1}{sin ( x )} 3

Simplificar

4 \cdot \frac{cos ( x )}{sin ( x )} - \frac{1}{sin ( x )} 3 : \frac{4 cos ( x ) - 3}{sin ( x )}

4 \cdot \frac{cos ( x )}{sin ( x )} - \frac{1}{sin ( x )} 3

4 \cdot \frac{cos ( x )}{sin ( x )} = \frac{4 cos ( x )}{sin ( x )}

4 \cdot \frac{cos ( x )}{sin ( x )}

Multiplicar fracciones:

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

= \frac{cos ( x ) \cdot 4}{sin ( x )}

\frac{1}{sin ( x )} 3 = \frac{3}{sin ( x )}

\frac{1}{sin ( x )} 3

Multiplicar fracciones:

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

= \frac{1 \cdot 3}{sin ( x )}

Multiplicar:

1 \cdot 3 = 3

= \frac{3}{sin ( x )}

= \frac{4 cos ( x )}{sin ( x )} - \frac{3}{sin ( x )}

Aplicar la regla

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

= \frac{4 cos ( x ) - 3}{sin ( x )}

= \frac{4 cos ( x ) - 3}{sin ( x )}

\frac{- 3 + 4 cos ( x )}{sin ( x )} = 0

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

- 3 + 4 cos (x) = 0

Mover

3

al lado derecho

- 3 + 4 cos (x) = 0

Sumar

3

a ambos lados

- 3 + 4 cos (x) + 3 = 0 + 3

Simplificar

4 cos (x) = 3

4 cos (x) = 3

Dividir ambos lados entre

4

4 cos (x) = 3

Dividir ambos lados entre

4

\frac{4 cos ( x )}{4} = \frac{3}{4}

Simplificar

cos (x) = \frac{3}{4}

cos (x) = \frac{3}{4}

Aplicar propiedades trigonométricas inversas

cos (x) = \frac{3}{4}

Soluciones generales para

cos (x) = \frac{3}{4}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

Mostrar soluciones en forma decimal

x = 1.12296 \dots + 2 πn, x = 2 π - 1.12296 \dots + 2 πn

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