verificar (sec^4(x)-1)/(tan^2(x))=tan^2(x)+2

Solución

verificar

\frac{sec ^{4} ( x ) - 1}{tan ^{2} ( x )} = tan^{2} (x) + 2

Verdadero

Pasos de solución

\frac{sec ^{4} ( x ) - 1}{tan ^{2} ( x )} = tan^{2} (x) + 2

Manipular el lado derecho

\frac{sec ^{4} ( x ) - 1}{tan ^{2} ( x )}

Re-escribir usando identidades trigonométricas

= tan^{2} (x) + 2

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

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

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

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

tan^{2} (x) - sec^{2} (x) = - 1

tan^{2} (θ) - sin^{2} (θ) = sin^{4} (θ) sec^{2} (θ)