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

Solución

verificar

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

Verdadero

Pasos de solución

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

Manipular el lado izquierdo

\frac{1}{cot ( x )}

Expresar con seno, coseno

\frac{1}{cot ( x )}

Utilizar la identidad trigonométrica básica:

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

= \frac{1}{\frac{c o s ( x )}{s i n ( x )}}

Simplificar

\frac{1}{\frac{c o s ( x )}{s i n ( x )}} : \frac{sin ( x )}{cos ( x )}

\frac{1}{\frac{c o s ( x )}{s i n ( x )}}

Aplicar las propiedades de las fracciones:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

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

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

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

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

(1 - cos (x)) (1 + sec (x)) = 1

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

cos^{2} (9 θ) - sin^{2} (9 θ) = cos (18 θ)

sec (x) csc (x) = 2 csc (2 x)