tan60*tan42*tan66*tan78=?

the angles are in degrees.

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).