Question

Would I have to use the Double-Angle Identity for sin in this problem?
Solve the equation 2sin(2x) = cos x

Answer 1

yes

you have 4sinxcosx = cos x

4sinx = 1

sin x = 1/4

you may have to write it as a general solution as there doesn't appear to be a given domain for x

Answer 2

\[4\cos(x)\sin(x)=\cos(x)\]
\[4\cos(x)\sin(x)-\cos(x)=0\]
\[cos(x)(4\sin(x)-1)=0\]
\[\cos(x)=0, \sin(x)=\frac{1}{4}\]

Answer 3

careful here. you cannot divide by cosine, because that gets rid of one of the solutions.
one solution is where \(\cos(x)=0\)

Answer 4

other you need \(\sin^{-1}(\frac{1}{4})\)

Answer 5

Thank you