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Determine the general solution for sin(x-30°)=cos2x

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Solution

- The solution steps are given below:

[tex]\begin{gathered} \sin(x-30)=\cos2x \\ \text{ The following trigonometric identities are used to proceed:} \\ \cos2x=\sin(90-2x) \\ \\ \sin(x-30)=\sin(90-2x) \\ \text{ We can proceed to equate the angles} \\ x-30=90-2x \\ \text{ Collect like terms} \\ 2x+x=90-30 \\ 3x=60 \\ \text{ Divide both sides by 3} \\ x=60 \end{gathered}[/tex]

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