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verificar cos(x)=(sin(2x))/(2sin(x))

Solución

verificar

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

Verdadero

Pasos de solución

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

Manipular el lado izquierdo

\frac{sin ( 2 x )}{2 sin ( x )}

Re-escribir usando identidades trigonométricas

\frac{sin ( 2 x )}{2 sin ( x )}

Utilizar la identidad trigonométrica del ángulo doble:

sin (2 x) = 2 sin (x) cos (x)

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

Simplificar

\frac{2 sin ( x ) cos ( x )}{2 sin ( x )} : cos (x)

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

Dividir:

\frac{2}{2} = 1

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

Eliminar los terminos comunes:

sin (x)

= cos (x)

= cos (x)

= cos (x)

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

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

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

\frac{cot ( θ ) tan ( θ )}{sec ( θ )} = cos (θ)

sin (a) cos (a) = cos^{2} (a) tan (a)

(cos (x)) (tan (x)) (csc (x)) = 1