show that tan 48 tan 23 tan 67=1
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The actual question that you were probably trying to ask was tan 48 x tan 42 x tan 23 x tan 67= 1.
In this case, tan 42 can be written as tan(90-48) = cot 48 = 1/tan48
Similarly, tan67 can be written as tan(90-67) = cot23 = 1/tan23
Putting all these terms together,
tan48 x 1/tan48 x tan23 x 1/tan23 cancels out totally leaving you with 1x1x1x1 = 1.