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cos3 210+cos3 39°Find the value of cos21 +cos 3 |
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Answer» (Cos^3 21°+ Cos^3 39°)/( cos 21 + cos 39°)=(cos 21° + cos 39°)(Cos^2 21° + Cos^2 39° -Cos 21 Cos 39°)/(Cos 21° + Cos 39°)=Cos²21°+Cos²39°-Cos21°Cos39°=1/2(2cos²21°+2cos²39°-2cos21°cos39°)=1/2[1+cos42°+1+cos78°-{cos(21°+39°)+cos(21°-39°)}][∵, 2cos²Ф=1+cos2Ф and 2cosAcosB=cos(A+B)+cos(A-B)]=1/2[2+cos42°+cos78°-cos60°-cos18°]=1/2[(2-1/2)+cos42°-cos18°+cos78°] ; [∵, cos60°=1/2]=1/2[3/2+{2sin(42°+18°)/2sin(18°-42°)}+cos78°] [∵, cosC-cosD=2sin(C+D)/2sin(D-C)/2]=1/2[3/2+2sin30°sin(-12°)+cos(90°-12°)]=1/2[3/2+2.1/2.(-sin12°)+sin12°] ; [∵, sin30°=1/2 and cos(90°-Ф)=sinФ]=1/2[3/2-sin12°+sin12°]=1/2×3/2=3/4 |
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