Transforme en producto y calcule sin 2 x − sin 5 x = 0

La ecuación dada es:

\[
\sin(2x) - \sin(5x) = 0
\]

Para transformarla en un producto, utilizamos la identidad trigonométrica:

\[
\sin(A) - \sin(B) = 2 \cos\left(\frac{A+B}{2}\right) \sin\left(\frac{A-B}{2}\right)
\]

En este caso, \(A = 5x\) y \(B = 2x\), así que:

\[
\sin(2x) - \sin(5x) = 2 \cos\left(\frac{5x + 2x}{2}\right) \sin\left(\frac{5x - 2x}{2}\right)
\]

Esto nos da:

\[
\sin(2x) - \sin(5x) = 2 \cos\left(\frac{7x}{2}\right) \sin\left(\frac{3x}{2}\right)
\]

Ahora la ecuación se transforma en

Explore the solution of the trigonometric equation sin(2x) − sin(5x) = 0. This involves using the product-to-sum identity to transform the expression and solve the equation. Ideal for students studying trigonometry in Grades 10-12.

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