1.

Prove the following : tan6^@.tan42^@.tan66^@.tan78^@ = 1

Answer»

SOLUTION :We have TAN3A
= tanAtan(60^@-A)tan(60^@+A)
Now putting `A=6^@` and `18^@`.
in (1) we have
`tan18^@=tan6^@tan54^@tan66^@......(2)
and `tan54^@`
=`tan18^@tan42^@tan78^@` ......(3)
Multiplying (2) and (3) we have
`tan18^@tan54^@`
=`tan6^@tan54^@tan66^@tan18^@tan42^@tan78^@`
or, 1=`tan6^@tan42^@tan66^@tan78^@`.


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