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Prove that sin10.sin30.sin50.sin70=1/16

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Prove that sin10.sin30.sin50.sin70=1/16

    • Posted by Mahesh Kumar 6 years, 3 months ago

    CBSE > Class 11 > Mathematics
    • 1 answers

    Pandat Viraj Bhardwaj 6 years, 3 months ago

    Sin10.sin30.sin50.sin.70=1/16 (Taking the value of sin30°= 1/2) also sin50°= sin60-10& sin70°= sin60+10(it can be written as this) 1/2 [ sin(60-10)sin(60+10)sin10° 1/2 [sin²60- Sin²10]sin10° 1/2[3/4 - sin²10]sin10°..( sin60=√3/2)&(√3/2)²= 3/4) Now 1/8[ 3sin10°- 4sin³] by using value of sin 3X 1/8 [sin3X] x= 10 1/8[sin3× 10] 1/8[ sin30°] ie. 1/8×1/2= 1/16 Hence proved... #PanDat_Golu❤

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