Question

Use a Double- or Half-Angle Formula to solve the equation in the interval $[0, 2\pi)$. \\ $\cos(2\theta) + \cos(\theta) = 2$

          Use a Double- or Half-Angle Formula to solve the equation in the interval $[0, 2\pi)$. \\
$\cos(2\theta) + \cos(\theta) = 2$
        
Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). 

cos(2θ) + cos(θ) = 2

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Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
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Use a Double- or Half-Angle Formula to solve the equation in the interval [0,2pi ). cos(2 heta )+cos( heta )=2 Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2T) cos(20)+cos)=2
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Transcript

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00:01 Hi there is a question we say that use double or half angle formula to solve the equation in the interval 0 to 2 pi we have 10 theta by 2 minus sine theta equal to 0.
00:16 We know that sine theta half angle formula will be 210 theta by 2 divide by 1 plus 10 square theta by 2 so let us plug in 10 theta by 2.
00:34 So let us plug in 10 theta by 2.
00:37 So let us plug in 10 theta by 2 minus 210 theta by 2 by 1 plus 10 square theta by 2 equal to 0 now 10 theta by 2 will be taken as common so 1 minus 2 divided by 1 plus 10 square theta by 2 equal to 0 either 10 theta by 2 equal to 0 or 1 minus 2 by 1 plus 10 square square theta by 2 equal to 0 now 10 theta by 2 equal to 0 so theta by 2 equal to k pi that means theta equal to 2k pi this is a end solution and from here 1 plus 10 square theta by 2 minus 2 equal to 0 so 10 square theta by 2 equal to 1 that means 10 square theta by 2 equal to 10 square pi by 4.
02:06 Now, we know that.
02:10 If 10 square theta equal to 10 square alpha, then theta becomes equal to k pi plus minus alpha, where k belongs to, of course, integers.
02:26 Here also, k belongs to the integers...
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