SOLUTION: Please help me find the exact value of this trig. function: 6sin75-6sin15

Question 749575: Please help me find the exact value of this trig. function: 6sin75-6sin15
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
6sin75-6sin15
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6*sin(30+45) - 6*sin(60-45)
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= 6[sin(30)(cos(45))+(cos(30)(sin(45)] - 6[sin(60)*cos(45)-cos(60)sin(45)]
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= 6[(1/2)(sqrt(2)/2)+(sqrt(3)/2)(sqrt(2)/2)]- 6[(sqrt(3)/2)(sqrt(2)/2)-(1/2)(sqrt(2)/2]
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= 6[sqrt(2)/4 + sqrt(6)/4] - 6[sqrt(6)/4 - sqrt(2/4]
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= 6[(sqrt(2)+sqrt(6))/4] - 6[(sqrt(6)-sqrt(2))/4]
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= (3/2)[sqrt(2)+sqrt(6)] - (3/2)[sqrt(6)-sqrt(2)]
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= 3*sqrt(2)
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Cheers,
Stan H.
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