Ashwin Muralidharan IIT Madras
Last Activity: 13 Years ago
Hi Aritra,
Here we use, tanxtan(60-x)tan(60+x) = tan3x -------{a standard formula}.
so consider tan18tan42tan78 = tan18tan(60-18)tan(60+18) = tan54.
So tan42tan78 = tan54/tan18-------(1)
Now consider tan6tan54tan66 = tan18.
So tan6tan66 = tan18/tan54-------(2)
Hence tan6tan42tan66tan78 = tan54/tan18 * tan18/tan54 = 1.
Note the first term is tan6, not tan60.
Hence value is 1.
Hope that helps.
All the best.
Regards,
Ashwin (IIT Madras).