SOLUTION: Using sum or difference formulas, find the exact value of cos(105∘). Express your answer in the form cos(105degrees)=a√(1−√b)/4 for some numbers a and b.
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Question 869667: Using sum or difference formulas, find the exact value of cos(105∘). Express your answer in the form cos(105degrees)=a√(1−√b)/4 for some numbers a and b.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Using sum or difference formulas, find the exact value of cos(105∘). Express your answer in the form cos(105degrees)=a√(1−√b)/4 for some numbers a and b.
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cos(105) = cos(50+45) = cos(60)*cos(45)-sin(60)*sin(45)
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= (1/2)(sqrt(2)/2) - (sqrt(3)/2)(sqrt(2)/2)
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= (1/4)(sqrt(2)) - (sqrt(6)/4)
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= (sqrt(2)-sqrt(6)/4
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Cheers,
Stan H.
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