Question

tan6 tan42 tan66 tan78 tan54

Answer 1

Method 1 -

Use Trigonometric Identity  

tanx * tan(60 - x) * tan(60 + x) = tan(3x)  

set x = 6  

tan6 * tan54 * tan66 = tan18 .................... ((1))  

Similarly, set x = 18  

tan18 * tan42 * tan78 = tan54 ...................... ((2))  

((1)) * ((2)):  

tan6 * tan54 * tan66 * tan18 * tan42 * tan78 = tan18 * tan54  

tan6 * tan66 * tan42 * tan78 = 1  
 

Method 2 -

Given - tan 6 tan 42 tan 66  tan 78