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Sagot :
Answer:
[tex]x=\frac{\pi}{2}+\pi n, \frac{\pi}{6}+2\pi n, \frac{5\pi}{6}+2\pi n[/tex]
Step-by-step explanation:
[tex]9sin(2x)=9cos(x)[/tex] <-- Starting Equation
[tex]9sin(2x)-9cos(x)=0[/tex] <-- Move all terms to the left and set equal to 0
[tex]9(sin(2x)-cos(x))=0[/tex] <--Simplify
[tex]9(2sin(x)cos(x)-cos(x))=0[/tex] <-- Trig Identity (sin2x=2sinxcosx)
[tex]9(cos(x)(2sin(x)-1)=0[/tex] <-- Simplify
[tex]9cos(x)(2sin(x)-1)=0[/tex] <-- Simplify
Use Zero Product Property:
[tex]9cos(x)=0[/tex] and [tex]2sin(x)-1=0[/tex]
Use the unit circle to find your solutions:
[tex]x=\frac{\pi}{2}+\pi n, \frac{\pi}{6}+2\pi n, \frac{5\pi}{6}+2\pi n[/tex]
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