verificar (1-cos(x))/(sin(x))=csc(x)-cot(x)

Solución

verificar

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

Verdadero

Pasos de solución

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

Manipular el lado izquierdo

csc (x) - cot (x)

Expresar con seno, coseno

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

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

cos^{2} (β) - sin^{2} (β) = 1 - 2 sin^{2} (β)

csc (2 x) = \frac{1}{2} sec (x) csc (x)

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

tan (2 a) = \frac{2 tan ( a )}{1 - tan ^{2} ( a )}

csc (x) - cot (x) = \frac{1}{csc ( x ) + cot ( x )}