Prove that `2 sin 2^(@)+4sin 4^(@)+6sin 6^(@)+........+180sin 180^(@)=90 cot 10^(@)`.

Explanation

`x=2 sin 2^(@)+4sin 4^(@)+6 sin 6^(@)+.....`
`+178 sin 178^(@)+180sin180^(@)`
`=(2 sin 2^(@)+178sin^(@))+(4sin 4^(@)+176sin 176^(@))`
`+(6sin6^(@)+174 sin 174^(@))`
`+(88sin 88^(@)+72 sin 72^(@))`
`=180(sin2^(@)+sin 4^(@)+sin6^(@)+......+sin 88^(@))+90`
`therefore x=180(sin""(44xx2^(@))/(2))/(sin 1^(@))sin(2^(@)+88^(@))/(2)+90`
`=90((2sin 44^(@)sin45^(@))/(sin1^(@))+1)=90((cos 1^(@)-cos89^(@))/(sin1^(@))+1)`
`=90(cot 1^(@)-(sin1^(@))/(sin1^(@))+1)=90cot 1^(@)`