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Multiplication of Cosine |
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Find the value of : cos(20)*cos(40)*cos(80)= ? Solution : cos(20*cos(40)*cos(80)=1/2*[cos(20+40)+cos(20-40)]*cos(80)= =1/2*[cos(60)+cos(-20)]*cos(80)= =1/2*[1/2+cos(20)]*cos(80)= =1/4*cos(8)+1/2*cos(20)*cos(80)= =1/4*cos(80)+1/4*[cos(20+80)+cos(20-80)]= =1/4*cos(80)+1/4*[cos(100)+cos(-60)]= =1/4*cos(80)+1/4*cos(100)+1/4*cos(60)= =1/4*cos(80)+1/4*cos(180-80)+1/8= =1/4*cos(80)-1/4*cos(80)+1/8=1/8 is final answer |
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