Really need help with this question! Been at it for a few days and not quite sure how to do it.
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http://mathurl.com/l4jo8p7.png
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Trigonometric Equations Help (1 Viewer)
- Thread starter ConHeo97
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Carrotsticks
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Move the sin(4x) over, so sin(x)+sin(3x)=sin(4x).
Now use something called a 'Sums to Products' formula (not in syllabus, but I'm surprised you got such a question all in one go).
Where A=3x and B=x.
Give it a try from here.
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Don't really need to know the sum to products formula (I never remember it myself) but more so how to arrive at that result.
sin 3x + sin x - sin 4x = 0
sin (2x + x) + sin (2x - x) - sin 4x = 0
sin 2x cos x + cos 2x sin x + sin 2x cos x - cos 2x sin x - sin 4x = 0
2sin 2x cos x - sin 4x = 0
2sin 2x cos x - 2sin 2x cos 2x = 0
2sin 2x (cos x - cos 2x) = 0
sin 3x + sin x - sin 4x = 0
sin (2x + x) + sin (2x - x) - sin 4x = 0
sin 2x cos x + cos 2x sin x + sin 2x cos x - cos 2x sin x - sin 4x = 0
2sin 2x cos x - sin 4x = 0
2sin 2x cos x - 2sin 2x cos 2x = 0
2sin 2x (cos x - cos 2x) = 0