verificar (csc(θ))/(sec(θ))=cot(θ)

Solución

verificar

\frac{csc ( θ )}{sec ( θ )} = cot (θ)

Verdadero

Pasos de solución

\frac{csc ( θ )}{sec ( θ )} = cot (θ)

Manipular el lado derecho

\frac{csc ( θ )}{sec ( θ )}

Expresar con seno, coseno

\frac{csc ( θ )}{sec ( θ )}

Utilizar la identidad trigonométrica básica:

csc (x) = \frac{1}{sin ( x )}

= \frac{\frac{1}{s i n ( θ )}}{sec ( θ )}

Utilizar la identidad trigonométrica básica:

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

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

Simplificar

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

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

Dividir fracciones:

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

= \frac{1 \cdot cos ( θ )}{sin ( θ ) \cdot 1}

Simplificar

= \frac{cos ( θ )}{sin ( θ )}

= \frac{cos ( θ )}{sin ( θ )}

= \frac{cos ( θ )}{sin ( θ )}

Utilizar la identidad trigonométrica básica:

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

= cot (θ)

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

sec (x) csc (x) = tan (x) + cot (x)

sin (x) \cdot sec (x) = tan (x)

cot (B) sin (B) = cos (B)

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

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