Mejia Davey
03/01/2024 · Senior High School
\( \cos ( 4 \theta ) \sin ( 3 \theta \)
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Tutor-Verified Answer
Step-by-step Solution
Para simplificar la expresión \( \cos(4\theta) \sin(3\theta) \), podemos utilizar la identidad del producto a suma. La identidad que nos puede ayudar es:
\[
\cos A \sin B = \frac{1}{2} [\sin(A + B) - \sin(A - B)]
\]
En este caso, \( A = 4\theta \) y \( B = 3\theta \). Aplicando la identidad, tenemos:
\[
\cos(4\theta) \sin(3\theta) = \frac{1}{2} [\sin(4\theta + 3\theta) - \sin(4\theta - 3\theta)]
\]
Simplificando los ángulos:
\[
= \frac{1}{2} [\sin(7\theta) - \sin(\theta)]
\]
Por lo tanto, la expresión simplificada es:
\[
\cos(4\theta) \sin(3\theta) = \frac{1}{2} [\sin(7\theta) - \sin(\theta)]
\]
Quick Answer
La expresión simplificada es \( \frac{1}{2} [\sin(7\theta) - \sin(\theta)] \).
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