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verificar-(cos^2(x))/(sin(x))=-cos(x)cot(x)

Solución

verificar

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

Verdadero

Pasos de solución

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

Manipular el lado izquierdo

- cos (x) cot (x)

Expresar con seno, coseno

- cos (x) cot (x)

Utilizar la identidad trigonométrica básica:

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

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

Simplificar

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

- cos (x) \frac{cos ( x )}{sin ( x )}

Multiplicar fracciones:

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

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

cos (x) cos (x) = cos^{2} (x)

cos (x) cos (x)

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

cos (x) cos (x) = cos^{1 + 1} (x)

= cos^{1 + 1} (x)

Sumar:

1 + 1 = 2

= cos^{2} (x)

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

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

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

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

tan^{3} (x) - tan (x) sec^{2} (x) = tan (- x)

sec (π - x) = - sec (x)

sin (- x) - cos (- x) = - (sin (x) + cos (x))

sec (a) - cos (a) csc (a) - sin (a) = tan (3 a)

cos^{2} (x) = sin (x)