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| 1. |
Prove that :- sin10°sin30°sin50°sin70° = 1/16 |
| Answer» LHS sin10 sin30 sin50 sin70Convert in cos by 90- angleFrom last Cos20 cos40 cos60 cos 80cos60=1/21/2 (cos20 cos40 cos80)Divide by 2sin20 1/2 (2sin20cos20 cos40 cos80/2sin20)1/2 (sin40cos40 cos80/2sin20)1/2 (2sin40cos40 cos80/2*2sin20)1/2 (sin80cos80/4sin20)1/2 (2sin80cos80/2*4sin20)1/2 (sin160/8sin20)Sin160=sin201/2 (sin20/8sin20)Sin20 cancel with sin201/2 (1/8)1/16RHS | |