verificar (sin(3x)-sin(5x))/(2cos(4x))=-sin(x)

Solución

verificar

\frac{sin ( 3 x ) - sin ( 5 x )}{2 cos ( 4 x )} = - sin (x)

Verdadero

Pasos de solución

\frac{sin ( 3 x ) - sin ( 5 x )}{2 cos ( 4 x )} = - sin (x)

Manipular el lado derecho

\frac{sin ( 3 x ) - sin ( 5 x )}{2 cos ( 4 x )}

Re-escribir usando identidades trigonométricas

= - sin (x)

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

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

tan (a) + cot (a) = 2 csc (2 a)

\frac{sec ^{2} ( t )}{csc ( t )} = sec (t) tan (t)

\frac{sec ( t ) - 1}{tan ( t )} = \frac{tan ( t )}{sec ( t ) + 1}

3 cos^{2} (x) - 3 sin^{2} (x) = 3 - 6 sin^{2} (x)