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verificar cot^2(x)cos^2(x)=cot^2(x)-cos^2(x)

Solución

verificar

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

Verdadero

Pasos de solución

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

Manipular el lado izquierdo

cot^{2} (x) - cos^{2} (x)

Expresar con seno, coseno

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

Factorizar

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

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

Re-escribir usando identidades trigonométricas

= \frac{cos ^{4} ( x )}{sin ^{2} ( x )}

Re-escribir usando identidades trigonométricas

cos^{2} (x) cot^{2} (x)

= cot^{2} (x) cos^{2} (x)

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

sin (a) = cos (9 0^{\circ} + a)

cot (θ) + tan (θ) = 2 csc (2 θ)

tan^{2} (a) - sin^{2} (a) = tan^{2} (a) sin^{2} (a)

cos (x) (tan (x) - sec (- x)) = sin (x) - 1

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