verificar sin(x)tan(x)=sec(x)-cos(x)

Solución

verificar

sin (x) tan (x) = sec (x) - cos (x)

Verdadero

Pasos de solución

sin (x) tan (x) = sec (x) - cos (x)

Manipular el lado derecho

sin (x) tan (x)

Expresar con seno, coseno

= \frac{sin ^{2} ( x )}{cos ( x )}

Re-escribir usando identidades trigonométricas

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

Manipular el lado izquierdo

sec (x) - cos (x)

Expresar con seno, coseno

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

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

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

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

\frac{csc ( x ) - cot ( x )}{sec ( x ) - 1} = cot (x)

\frac{1 + cos ( x )}{1 - cos ( x )} - \frac{1 - cos ( x )}{1 + cos ( x )} = 4 cot (x) csc (x)

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