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

Solución

verificar

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

Verdadero

Pasos de solución

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

Manipular el lado izquierdo

1 - cot (x)

Expresar con seno, coseno

1 - cot (x)

Utilizar la identidad trigonométrica básica:

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

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

Simplificar

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

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

Convertir a fracción:

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

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

Ya que los denominadores son iguales, combinar las fracciones:

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

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

Multiplicar:

1 \cdot sin (x) = sin (x)

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

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

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

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

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

\frac{( sec ( θ ) - 1 )}{( 1 - cos ( θ ) )} = sec (θ)

cos (0) tan (0) = sin (0)

cos (\frac{π}{6}) = \frac{4}{3} cos^{3} (\frac{π}{6})

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

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