Question

find the value of n,if (sin 1)(sin 3)(sin 5)(sin 7).....(sin 89) =1/2n

Answer 1

This question is related to trignometric functions , in math they are usually the functions of the angles. Here we would be using trignometric identities, they are generally equalities.
Now for the value of 'n' we have the following solution:

= sin1. sin2. sin3. sin4. sin5. sin 7...sin88. sin89/Sin 2.sin4.sin6.. sin88
=(sin1.sin89).(sin2.sin88).(sin3.sin87).(sin4.sin86)...(sin44.sin46).(sin45) / (sin2.sin4.sin6.sin8...sin88)
=(sin1 .cos1).(sin2.cos2).(sin3.cos3).(sin4.cos4)....(sin44.cos44)..sin45 / 2^44.sin2.sin4.sin6.sin8..sin88
=sin 45/2^44
Thus,
=1/(√2)*(2^44)
$1 \div {2}^{89 \div 2}$
Hence the value of n will be 89/2 for the above equation.