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verificar-2cos(x)sec^2(x)=-2/(cos(x))

Solución

verificar

- 2 cos (x) sec^{2} (x) = - \frac{2}{cos ( x )}

Verdadero

Pasos de solución

- 2 cos (x) sec^{2} (x) = - \frac{2}{cos ( x )}

Manipular el lado derecho

- 2 cos (x) sec^{2} (x)

Expresar con seno, coseno

- 2 cos (x) sec^{2} (x)

Utilizar la identidad trigonométrica básica:

sec (x) = \frac{1}{cos ( x )}

= - 2 cos (x) (\frac{1}{cos ( x )})^{2}

Simplificar

- 2 cos (x) (\frac{1}{cos ( x )})^{2} : - \frac{2}{cos ( x )}

- 2 cos (x) (\frac{1}{cos ( x )})^{2}

(\frac{1}{cos ( x )})^{2} = \frac{1}{cos ^{2} ( x )}

(\frac{1}{cos ( x )})^{2}

Aplicar las leyes de los exponentes:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{cos ^{2} ( x )}

Aplicar la regla

1^{a} = 1

1^{2} = 1

= \frac{1}{cos ^{2} ( x )}

= - 2 \cdot \frac{1}{cos ^{2} ( x )} cos (x)

Multiplicar fracciones:

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

= - \frac{1 \cdot 2 cos ( x )}{cos ^{2} ( x )}

Multiplicar los numeros:

1 \cdot 2 = 2

= - \frac{2 cos ( x )}{cos ^{2} ( x )}

Eliminar los terminos comunes:

cos (x)

= - \frac{2}{cos ( x )}

= - \frac{2}{cos ( x )}

= - \frac{2}{cos ( x )}

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

1 + sin (4 a) + sin (2 a) = sin (2 a)

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

\frac{6 tan ( x ) + 6 cot ( y )}{tan ( x ) cot ( y )} = 6 tan (y) + 6 cot (x)

tan^{2} (x) sin^{2} (x) = tan^{2} (x) + sin^{2} (x)

cos (- \frac{π}{6}) = sin (- \frac{π}{6} + \frac{π}{2})