verificar cos(x)cot(x)=(1-sin^2(x))/(sin(x))

Solución

verificar

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

Verdadero

Pasos de solución

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

Manipular el lado derecho

cos (x) cot (x)

Expresar con seno, coseno

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

Re-escribir usando identidades trigonométricas

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

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

2 sin^{2} (x) + cos (2 x) = 1

\frac{1 + sec ( x )}{sin ( x ) + tan ( x )} = csc (x)

\frac{tan ^{2} ( x )}{1 + tan ^{2} ( x )} = sin^{2} (x)

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

tan (\frac{π}{2} - x) sec (x) = csc (x)