verificar (sec(x))/(csc(x))+(sin(x))/(cos(x))=2tan(x)

Solución

verificar

\frac{sec ( x )}{csc ( x )} + \frac{sin ( x )}{cos ( x )} = 2 tan (x)

Verdadero

Pasos de solución

\frac{sec ( x )}{csc ( x )} + \frac{sin ( x )}{cos ( x )} = 2 tan (x)

Manipular el lado derecho

\frac{sec ( x )}{csc ( x )} + \frac{sin ( x )}{cos ( x )}

Expresar con seno, coseno

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

Re-escribir usando identidades trigonométricas

2 tan (x)

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

\frac{sin ( θ ) + tan ( θ )}{1 + sec ( θ )} = sin (θ)

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

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

tan (θ) + cot (θ) = sec (θ) \cdot csc (θ)

\frac{cos ( x )}{csc ( x ) + 1} + \frac{cos ( x )}{csc ( x ) - 1} = 2 tan (x)