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(7) Prove thatcos 20° cos 40 cos 60 .cos 8016 |
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Answer» cos20°cos40°cos60°cos80°=(1/2)(2cos20°cos40°)(1/2)cos(80°){cos60°=1/2; and multiplying and dividing by 2}=(1/4){cos(20°+40°)+cos(40°-20°)}cos80°=(1/4){cos60°+cos20°}cos80°=(1/4){(1/2)cos80°+cos20°cos80°}=(1/4)(1/2)cos80°+(1/4)cos20°cos80°=(1/8)cos80°+(1/4)(1/2){2cos20°cos80°}=(1/8)cos80°+(1/8){cos (80+20)+cos(80-20)}=(1/8)cos80°+(1/8){cos100°+cos60°}=(1/8)cos80°+(1/8)cos100°+(1/8)(1/2)=(1/8){cos80°+cos100°}+1/16=(1/8){2cos((100°+80°)/2)cos((100°-80°)/2)}+1/16=(1/8){2cos90°cos10°}+1/16=1/16 you not seen problem carefully |
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