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sin(x)cot(x)csc(x)=sqrt(2)

Solución

sin (x) cot (x) csc (x) = 2

x = 0.61547 \dots + πn

Grados

x = 35.26438 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

sin (x) cot (x) csc (x) = 2

Re-escribir usando identidades trigonométricas

sin (x) cot (x) csc (x)

csc (x) sin (x) = 1

csc (x) sin (x)

Expresar con seno, coseno

csc (x) sin (x)

Utilizar la identidad trigonométrica básica:

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

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

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

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

Multiplicar fracciones:

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

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

Eliminar los terminos comunes:

sin (x)

= 1

= 1

= cot (x) \cdot 1

cot (x) \cdot 1 = 2

Multiplicar:

cot (x) \cdot 1 = cot (x)

cot (x) = 2

Aplicar propiedades trigonométricas inversas

cot (x) = 2

Soluciones generales para

cot (x) = 2

cot (x) = a \Rightarrow x = arccot (a) + πn

x = arccot (2) + πn

x = arccot (2) + πn

Mostrar soluciones en forma decimal

x = 0.61547 \dots + πn

cos (2 x) + 4 cos (x) = - 3

1 = 2 cos (2 x)

cos (\frac{π}{6}) = sin (x)

cos (θ) = - \frac{9}{10}

arctan (x) = \frac{1}{2}