floor equation.

1cos 40+1cos 80+1cos 160

=1cos 40+1cos 80-1cos 20

=cos 40+cos 80cos 40 x cos 80-1cos 20

=2cos 60 x cos 20cos 40 x cos 80-1cos 20

=cos²20- (cos 40 x cos 80)cos 40 x cos 80 x cos 20

=cos²20- (cos(60-20) x cos (60+20))cos 40 x cos 80 x cos 20

now using cos(a+b)cos(a-b)=cos²b=sin²a

we get sin²60cos 40 x cos 80 x cos 20

now we can easily prove that cos 40 x cos 80 x cos 20 is equal to 18 by using the trick of multiplying sin 20 in the numerator and denominator......

thus we get the given expression sec 40+sec 80+sec 160 equal to 6....