Question

tan48 tan 23 tan 42 tan 67=1

Answer 1

HOPE IT WILL HELP YOU.........

Answer 2

Hi use the following identities
$\ \ \tan (90 - x) = \ \ \cot(x) \\ \cot(x) = \frac{1}{ \tan(x) }$
Now
$\tan(48) = \tan(90 - 42) = \cot(42) \\ = \frac{1}{ \tan(42) }$
and
$\tan(23) = \tan(90 - 67) = \cot(67) \\ = \frac{1}{ \tan(67) }$
Therefore
$\tan(48) \tan(23) \tan(42) \tan(67) = \\ \frac{1}{ \tan(42) } \times \frac{1}{ \tan(67) } \times \tan(42) \times \tan(67) \\ = 1$