verificar csc(x)=(1+sec(x))/(sin(x)+tan(x))

Solución

verificar

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

Verdadero

Pasos de solución

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

Manipular el lado izquierdo

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

Expresar con seno, coseno

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

Re-escribir usando identidades trigonométricas

csc (x)

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

tan^{2} (θ) + 6 = sec^{2} (θ) + 5

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

sec (\frac{π}{2} - x) = csc (x)

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

\frac{1 + cos ( t )}{1 - cos ( t )} = (csc (t) + cot (t))^{2}