Question

prove that, tan 6 tan 42 tan 66 tan 78 = 1

Answer 1

given
L.H.S=tan 6 tan 42 tan 66  tan 78
now ,

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 
Hence
L.H.S=R.H.S
proved

Answer 2

Answer:

Here is your answer buddy....