verificar sec(x)(sec(x)-cos(x))=tan^2(x)

Solución

verificar

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

Verdadero

Pasos de solución

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

Manipular el lado derecho

sec (x) (sec (x) - cos (x))

Expandir

(- cos (x) + sec (x)) sec (x) : - sec (x) cos (x) + sec^{2} (x)

= sec^{2} (x) - cos (x) sec (x)

Re-escribir usando identidades trigonométricas

= tan^{2} (x)

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

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

sin (3 x) = 3 sin (x) - 4 (sin (x))^{3}

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

cot (x) \cdot sec (x) = csc (x)

2 - csc^{2} (θ) = 1 - cot^{2} (θ)