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26 votes
26 votes
Solve in radians for 6sin2(x)=6cos(x)

User Diatoid
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1 Answer

17 votes
17 votes

An important trigonometric function is sin(2x):


\sin (2x)=2\cdot\sin x\cdot\cos x

Let's use it to solve the given equation.


\begin{gathered} 6\cdot\sin (2x)=6\cos x \\ 6\cdot2\cdot\sin x\cdot\cos x=6\cos x \\ \sin x=(6\cdot\cos x)/(2\cdot6\cdot\cos x) \\ \sin x=(1)/(2) \\ x=\sin ^(-1)((1)/(2)) \\ x=(\pi)/(6) \end{gathered}

User Corbee
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