Question

Prove that
tan48 x tan23 x tan42 x tan67=1

Answer 1

We know that tan(90- theta) = cot theta = 1/tan theta

Here tan 48 = tan (90-42) = cot 48

And tan 23 = tan (90-67) = cot 67

So, if we multiply all the terms, we get (tan 48)(cot 48) =1

(tan 67)(cot67)= 1

LHS = 1 = RHS

Hence proved

Hope this helps!