SOLUTION: Prove that tan(10°)cos(20°)tan(40°)tan(50°)csc(70°)sec(80°)sin(80°) = 1

Prove that tan(10°)cos(20°)tan(40°)tan(50°)csc(70°)sec(80°)sin(80°) = 1

Change all trig ratios other than the sines and cosines
to sines and cosines, and put 1 denominators under the 
sines and cosines, using these quotient and reciprocal 
identities: 

, , 



Next change all the cosines to sines using the cofuction identity:









Substitute those for all the cosines:



That all cancels and gives 1

Edwin