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Prove thatsin10.sin30.sin50.sin70=1/16 |
| Answer» 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 3X1/8 [sin3X] x= 101/8[sin3× 10]1/8[ sin30°]ie. 1/8×1/2= 1/16 Hence proved... #PanDat_Golu❤ | |