`((sin 33^(@))/( sin 11^(@) sin 49^(@) sin 71^(@)))^(2) + (( cos 33^(@))/(cos 11^(@) cos 49^(@) cos 71^(@)))^(2) ` is equal to ______.

Answer

32

Explanation

Given expression is `(( sin 33^(@))/(sin 11^(@) sin ( 60^(@) - 11^(@)) sin (60+11^(@))))^(2) + (( cos 33^(@))/( cos 11^(@) cos ( 60^(@) - 11^(@)) cos ( 60^(@) + 11^(@)))) ^(2)`
`= (( sin 33^(@))/( (1)/(4) sin 33^(@)))^(2) + ( ( cos 33^(@))/( (1)/(4) cos 33^(@)))^(2)`
` = 16 + 16 = 32`