IIT JEE , AIEEE Forum - Mathematics , Trignometry

phanindraramesh

For

tan6tan42tan66tan78

Try to prove tanxtan(60-x)tan(60+x)=tan3x

multiply n divide with tan18tan54

we will get

[tan6 tan54 tan66][tan18 tan42 tan78]

-------------------------------------------------------

tan18 tan54

=---------------------

tan18tan54

=1

i think the problem was completed

PROOF OF tanx tan(60-x)tan(60+x)=tan3x :-

---------------------------------------------------------------

tanx tan60-tanx tan60+tanx

--------------- ------------------

1+tan60tanx 1+tan60tanx

tanx tan²60-tan²x

= --------------------

1-tan²60tan²x

tanx 3-tan²x

= -----------

1-3tanx

3tanx-tan³x

= -----------------

1-3tanx

=tan3x

I think it is clear

BYE............................