verificar csc^2(x)+2cot(x)=(1+cot(x))^2

Solución

verificar

csc^{2} (x) + 2 cot (x) = (1 + cot (x))^{2}

Verdadero

Pasos de solución

csc^{2} (x) + 2 cot (x) = (1 + cot (x))^{2}

Manipular el lado derecho

csc^{2} (x) + 2 cot (x)

Re-escribir usando identidades trigonométricas

= 1 + cot^{2} (x) + 2 cot (x)

Manipular el lado izquierdo

(1 + cot (x))^{2}

Expandir

(1 + cot (x))^{2} : 1 + 2 cot (x) + cot^{2} (x)

= 1 + cot^{2} (x) + 2 cot (x)

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

csc (t) cot (t) = \frac{1 + cot ^{2} ( t )}{sec ( t )}

csc (a) sec (a) = 2 csc (2 a)

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

tan^{2} (2 x) + 1 = sec^{2} (2 x)

sin (4 θ) = 4 sin (θ) cos (θ) cos (2 θ)