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verificar sin(2a)+cos(a)=cos(a)(2sin(a)+1)

Solución

verificar

sin (2 a) + cos (a) = cos (a) (2 sin (a) + 1)

Verdadero

Pasos de solución

sin (2 a) + cos (a) = cos (a) (2 sin (a) + 1)

Manipular el lado derecho

sin (2 a) + cos (a)

Re-escribir usando identidades trigonométricas

sin (2 a) + cos (a)

Utilizar la identidad trigonométrica del ángulo doble:

sin (2 x) = 2 sin (x) cos (x)

= 2 sin (a) cos (a) + cos (a)

= 2 sin (a) cos (a) + cos (a)

Manipular el lado izquierdo

cos (a) (2 sin (a) + 1)

Expandir

(1 + 2 sin (a)) cos (a) : cos (a) + 2 cos (a) sin (a)

(1 + 2 sin (a)) cos (a)

= cos (a) (1 + 2 sin (a))

Poner los parentesis utilizando:

a (b + c) = ab + a c

a = cos (a), b = 1, c = 2 sin (a)

= cos (a) \cdot 1 + cos (a) \cdot 2 sin (a)

= 1 \cdot cos (a) + 2 cos (a) sin (a)

Multiplicar:

1 \cdot cos (a) = cos (a)

= cos (a) + 2 cos (a) sin (a)

= cos (a) + 2 cos (a) sin (a)

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

\frac{csc ( x )}{2 cos ( x )} = csc (2 x)

tan^{2} (u) = \frac{1 - cos ( 2 u )}{1 + cos ( 2 u )}

(1 + sin (θ)) (1 - sin (θ)) = \frac{1}{sec ^{2} ( θ )}

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

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