Sin 1+sin 2+sin3............sin89
Dhruv00:
R u sure that there is +sign in between
Answers
Answered by
4
Pair products of sines whose degrees add up to 90 i.e.
Sin(1)*Sin(2)*Sin(3)*...*Sin(89)=sin(1)*sin(89) * sin(2)*sin(88) * .... * sin(44)*sin(46) *sin(45)
Use the trigonometric product to sum formula, and cos(90)=0 to obtain
2^(-44) * cos(88)*cos(86)*cos(84)* ... *cos(2) * sin(45) = 2^(-44.5) * cos(88)*cos(2) * cos(86)* cos(4) * ... cos(46)*cos(44)
I guess that successive application of the product to sum forumula can now be used, but am too lazy to investigate further.
Numerical calculation gives an answer of about ~ 2^(-85.75) if it's any help
Sin(1)*Sin(2)*Sin(3)*...*Sin(89)=sin(1)*sin(89) * sin(2)*sin(88) * .... * sin(44)*sin(46) *sin(45)
Use the trigonometric product to sum formula, and cos(90)=0 to obtain
2^(-44) * cos(88)*cos(86)*cos(84)* ... *cos(2) * sin(45) = 2^(-44.5) * cos(88)*cos(2) * cos(86)* cos(4) * ... cos(46)*cos(44)
I guess that successive application of the product to sum forumula can now be used, but am too lazy to investigate further.
Numerical calculation gives an answer of about ~ 2^(-85.75) if it's any help
sign is + not ×
Similar questions