Cos10.cos30.cos50.cos70=3/16

Asked by Sandeep | 18th Sep, 2015, 12:47: PM

Expert Answer:

begin mathsize 14px style cos 10. cos 30. cos 50. cos 70 equals cos 30. cos 70 left parenthesis cos 50. cos 10 right parenthesis equals fraction numerator square root of 3 over denominator 2 end fraction cos 70 cross times 1 half left parenthesis cos 60 plus cos 40 right parenthesis equals fraction numerator square root of 3 over denominator 4 end fraction cos 70 open parentheses 1 half plus cos 40 close parentheses equals fraction numerator square root of 3 over denominator 4 end fraction open square brackets 1 half cos 70 plus cos 70. cos 40 close square brackets equals fraction numerator square root of 3 over denominator 4 end fraction open square brackets 1 half cos 70 plus 1 half left parenthesis cos 110 plus cos 30 right parenthesis close square brackets equals fraction numerator square root of 3 over denominator 4 end fraction open square brackets 1 half cos 70 plus 1 half left parenthesis negative cos 70 plus fraction numerator square root of 3 over denominator 2 end fraction right parenthesis close square brackets equals fraction numerator square root of 3 over denominator 4 end fraction open square brackets 1 half cos 70 minus 1 half cos 70 plus fraction numerator square root of 3 over denominator 4 end fraction close square brackets equals 3 over 16 end style

Answered by Rashmi Khot | 18th Sep, 2015, 04:42: PM