verificar (cos^2(x)-1)(tan^2(x)+1)=-tan^2(x)

Solución

verificar

(cos^{2} (x) - 1) (tan^{2} (x) + 1) = - tan^{2} (x)

Verdadero

Pasos de solución

(cos^{2} (x) - 1) (tan^{2} (x) + 1) = - tan^{2} (x)

Manipular el lado derecho

(cos^{2} (x) - 1) (tan^{2} (x) + 1)

Expandir

(- 1 + cos^{2} (x)) (1 + tan^{2} (x)) : - 1 - tan^{2} (x) + cos^{2} (x) + cos^{2} (x) tan^{2} (x)

= - 1 + cos^{2} (x) - tan^{2} (x) + cos^{2} (x) tan^{2} (x)

Re-escribir usando identidades trigonométricas

= - tan^{2} (x)

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

7 csc^{2} (θ) - 5 cot^{2} (θ) = 2 csc^{2} (θ) + 5

cos (θ) = \frac{cot ( θ )}{csc ( θ )}

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

cos (x - \frac{3 π}{2}) = - sin (x)

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