We know that cot(90∘−θ)=tanθ
∴tan48∘.tan23∘.tan42∘.tan67∘
= tan48∘.tan23∘.cot(90∘−42∘).cot(90∘−67∘)
= tan48∘.tan23∘.cot48∘.cot23∘
We also know that tanθ×cotθ=1
∴tan48∘.tan23∘.cot48∘.cot23∘
= tan48∘.cot48∘.tan23∘.cot23∘
= 1×1
= 1
Thus, tan48∘.tan23∘.tan42∘.tan67∘=1