verificar sin^2(θ/2)=(csc(θ)-cot(θ))/(2csc(θ))

Solución

verificar

sin^{2} (\frac{θ}{2}) = \frac{csc ( θ ) - cot ( θ )}{2 csc ( θ )}

Verdadero

Pasos de solución

sin^{2} (\frac{θ}{2}) = \frac{csc ( θ ) - cot ( θ )}{2 csc ( θ )}

Sea:

u = \frac{θ}{2}

sin^{2} (u) = \frac{csc ( 2 u ) - cot ( 2 u )}{2 csc ( 2 u )}

Verificar

sin^{2} (u) = \frac{csc ( 2 u ) - cot ( 2 u )}{2 csc ( 2 u )} :

Verdadero

Por lo tanto

sin^{2} (\frac{θ}{2}) = \frac{csc ( θ ) - cot ( θ )}{2 csc ( θ )}

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

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

sin^{2} (x) - 2 cos^{2} (x) = 3 sin^{2} (x) - 2

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

tan (a) = tan (a) csc^{2} (a) + cot (- a)

7 csc^{2} (x) - 5 cot^{2} (x) = 2 csc^{2} (x) + 5