Question

Prove that

sin20°sin 40°sin80° sin90°= √3/8
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Answer 1

Step-by-step explanation:

sin 90°{sin20°sin40°} sin80°

multiply by 2in this eq.

we will apply formula of 2sinAsinB=cos(a-b)-cos(a+b)

1*1/2{cos20°-cos60°}sin 80°

1*1/2{sin80°cos20°-1/2sin80°}

1/2*1/2{2sin80°cos20°-sin80°}

we will apply formula 2sinAcosB=sin(a+b)+sin(a-b)

1/4{sin 100°+sin60°-sin80°}

sin (180°-80°)=100° so we will write sin 80°in place of 100°

1/4{sin80°+sin60°-sin80°}

1/4*sin 60°= (/√3/4) so

√3/2*1/4=√3/8

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