verificar (tan(θ)+cot(θ))/(tan(θ))=csc^2(θ)

Solución

verificar

\frac{tan ( θ ) + cot ( θ )}{tan ( θ )} = csc^{2} (θ)

Verdadero

Pasos de solución

\frac{tan ( θ ) + cot ( θ )}{tan ( θ )} = csc^{2} (θ)

Manipular el lado derecho

\frac{tan ( θ ) + cot ( θ )}{tan ( θ )}

Expresar con seno, coseno

= \frac{cos ^{2} ( θ ) + sin ^{2} ( θ )}{sin ^{2} ( θ )}

Re-escribir usando identidades trigonométricas

= \frac{1}{sin ^{2} ( θ )}

Re-escribir usando identidades trigonométricas

csc^{2} (θ)

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

sin (6 0^{\circ}) = 2 sin (3 0^{\circ}) cos (3 0^{\circ})

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

cos (x) \cdot tan (x) = sin (x)

\frac{sin ( 2 θ )}{sin ( θ )} - \frac{cos ( 2 θ )}{cos ( θ )} = sec (θ)

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