Question

Tan48degree*tan23degree*tan42degree*tan67degree= 1

Answer 1

tan48°×tan23°×tan42°×tan67°=1
L.H.S
(tan48°×tan42°)×(tan23°×tan67°)
(tan48°×tan (90°-42°) × (tan23°×tan (90°-67°)
(tan48°×cot48°) × (tan23°×cot23°)
(tan48°×1/tan48°) × (tan23°×1/tan23°)
1×1
=1
L.H.S = R.H.S

Answer 2

Given,
Tan48°×tan23°×tan42°×tan67°
We know that tan(90-ø)= cotø as it lies in first quadrant.
see picture!.
Hope it helped you!!