verificar (2sin(x)+cos(x))^2+(2cos(x)-sin(x))^2=5

Solución

verificar

(2 sin (x) + cos (x))^{2} + (2 cos (x) - sin (x))^{2} = 5

Verdadero

Pasos de solución

(2 sin (x) + cos (x))^{2} + (2 cos (x) - sin (x))^{2} = 5

Manipular el lado derecho

(2 sin (x) + cos (x))^{2} + (2 cos (x) - sin (x))^{2}

Factorizar

(- sin (x) + 2 cos (x))^{2} + (cos (x) + 2 sin (x))^{2} : 5 (sin^{2} (x) + cos^{2} (x))

= (cos^{2} (x) + sin^{2} (x)) \cdot 5

Re-escribir usando identidades trigonométricas

= 5

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

cos (a) (sec (a) - cos (a)) = sin^{2} (a)

tan (x) cos (x) csc (x) = 1

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

\frac{csc ^{4} ( x ) - 1}{1 + csc ^{2} ( x )} = cot^{2} (x)

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