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For the following exercises, solve with the methods shown in this section exactly on the interval $[0, 2\pi)$. 33. $\sin(3x)\cos(6x) - \cos(3x)\sin(6x) = -0.9$ 35. $\cos(2x)\cos x + \sin(2x)\sin x = 1$ 37. $9\cos(2\theta) = 9\cos^2 \theta - 4$ 39. $\cos(2t) = \sin t$ 34. $\sin(6x)\cos(11x) - \cos(6x)\sin(11x) = -0.1$ 36. $6\sin(2t) + 9\sin t = 0$ 38. $\sin(2t) = \cos t$ 40. $\cos(6x) - \cos(3x) = 0$

          For the following exercises, solve with the methods shown in this section exactly on the interval $[0, 2\pi)$. 
33. $\sin(3x)\cos(6x) - \cos(3x)\sin(6x) = -0.9$
35. $\cos(2x)\cos x + \sin(2x)\sin x = 1$
37. $9\cos(2\theta) = 9\cos^2 \theta - 4$
39. $\cos(2t) = \sin t$
34. $\sin(6x)\cos(11x) - \cos(6x)\sin(11x) = -0.1$
36. $6\sin(2t) + 9\sin t = 0$
38. $\sin(2t) = \cos t$
40. $\cos(6x) - \cos(3x) = 0$
        
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For the following exercises, solve with the methods shown in this section exactly on the interval [0, 2π). 
33. sin(3x)cos(6x) - cos(3x)sin(6x) = -0.9
35. cos(2x)cos x + sin(2x)sin x = 1
37. 9cos(2θ) = 9cos^2 θ - 4
39. cos(2t) = sin t
34. sin(6x)cos(11x) - cos(6x)sin(11x) = -0.1
36. 6sin(2t) + 9sin t = 0
38. sin(2t) = cos t
40. cos(6x) - cos(3x) = 0

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Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
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For the following exercises, solve with the methods shown in this section exactly on the interval [0,2pi ). 40. cos(6x)-cos(3x)=0 For the following exercises,solve with the methods shown in this section exactly on the interval [0,2n) 33.sin3xcos6x-cos3xsin6x=-0.9 34.sin6xcos11x-cos6xsin11x=-0.1 35.cos2xcosx+sin2xsinx=1 36.6sin2t+9sint=0 37.9cos20=9cos-4 38.sin2t=cost 39.cos2t=sin t 40.cos6xcos3x=0
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Transcript

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00:01 All right, so we're given cosine of 2x times the cosine of x plus the sine of 2x times a sign of x equals 1.
00:09 And we are trying to see what this holds true between 0 included and 2 pi not included.
00:16 So the first thing, i want to read both the cosine 2x and the sine 2x.
00:21 So the cosine of 2x, we're going to go ahead and we're going to let that equal.
00:31 We'll say 2 cosine squared x minus 1.
00:40 I actually want to keep us all in terms of sine and cosine.
00:43 So we're going to change that real quick to 2.
00:50 2x cosine x times cosine x plus the sine 2x becomes 2x cosine x becomes 2x cosine x times sine x must equal 1...
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