verificar-sin^2(x)sec^2(x)=1-sec^2(x)

Solución

verificar

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

Verdadero

Pasos de solución

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

Manipular el lado derecho

- sin^{2} (x) sec^{2} (x)

Re-escribir usando identidades trigonométricas

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

Expandir

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

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

Re-escribir usando identidades trigonométricas

= 1 - sec^{2} (x)

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

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

sin^{2} (θ) + sin^{2} (θ) tan^{2} (θ) = tan^{2} (θ)

1 + sin (2 θ) = (cos (θ) sin (θ))^{2}

sec (θ) csc (θ) = tan (θ) + cot (θ)

2 tan (0^{\circ}) = sin (0^{\circ})