prove that sin 10*sin 30*sin 50 *sin 70= 1/16

1.	prove that sin 10sin 30sin 50 *sin 70= 1/16
Answer» We know thati) sin 2A = 2sinAcosAii) sin(90-A)= cosAiii) sin30=1/2LHS = sin 10 sin30 sin50sin 70=sin 10 × 1/2 × sin (90-40)× sin(90-20)=1/2[sin 10 ×cos 40×cos 20]We multiply with[2 cos 10/2cos 10]=(1/2×1/2cos10)[2sin10cos10×cos20×cos40]=(1/4cos10)[sin20cos20×cos40]=(1/8cos10)[2sin20cos20×cos40]=(1/8cos10)[sin40cos40]=(1/16cos10)[2sin40co40]=(1/16cos10)×sin80=(1/16cos10)×sin(90-10)=(1/16cos10)×cos10=1/16= RHS

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