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To solve the equation [tex]3 \sin(2x) = 5 \cos(x)[/tex], you should rewrite it as:

A. [tex]\cos(x)(6 \sin(x) - 5) = 0[/tex]
B. [tex]\cos(x)(3 \sin(x) - 5) = 0[/tex]
C. [tex]3 \sin(x) + 5 \cos(x) = 0[/tex]

Sagot :

GinnyAnsweridn
To solve the equation [tex]\(3 \sin(2x) = 5 \cos(x)\)[/tex], let's go through the process step-by-step to rewrite it in the appropriate form.

1. Use the double-angle identity for sine:
[tex]\[\sin(2x) = 2 \sin(x) \cos(x)\][/tex]

2. Substitute this identity into the given equation:
[tex]\[3 \sin(2x) = 5 \cos(x)\][/tex]
[tex]\[3 \cdot 2 \sin(x) \cos(x) = 5 \cos(x)\][/tex]

3. Simplify the left-hand side of the equation:
[tex]\[6 \sin(x) \cos(x) = 5 \cos(x)\][/tex]

4. Factor out [tex]\(\cos(x)\)[/tex] from both sides of the equation:
[tex]\[\cos(x) \left(6 \sin(x) - 5\right) = 0\][/tex]

Therefore, the equation [tex]\(3 \sin(2x) = 5 \cos(x)\)[/tex] can be rewritten as:

[tex]\[ \cos(x) (6 \sin x - 5) = 0 \][/tex]

So, the correct answer is:

A. [tex]\(\cos x(6 \sin x - 5)=0\)[/tex]
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