Multiplication of Cosine
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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