1.

3n 4n23. Prove that cos — cos —— €0S —o— €08 = - .9 9 9 9

Answer»

sin(π/9)*cos(π/9)*cos(2π/9)*cos(3π/9)*cos(4π/9)/sin(π/9)=sin(2π/9)cos(2π/9)*cos(3π/9)*cos(4π/9)/[2*sin(π/9)]=sin(4π/9)*cos(3π/9)*cos(4π/9)/[4*sin(π/9)]=sin(8π/9)*cos(3π/9)/[8*sin(π/9)]=sin(π/9)*cos(3π/9)/[8*sin(π/9)]=cos(3π/9)/8=1/16

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