Question

Show that
tan48× tan23× tan67= 1

Answer 1

=tan48×tan(90-67)×tan67

=tan48×cot67×tan67

=tan48

that's the answer man

Answer 2

I think there must be tan42° so the product will be 1.

tan48°×tan23°×tan42°×tan67° = 1

Solving LHS,

We know that 48+42 = 90

hence, 42 = 90-48

and 67+23 = 90

67 = 90-23

Now, substitutes those value but now there will be a cot sign, so

tan 48°×cot 48°×tan 23°× cot 23°

Here tan and cot will be cancel out so,

1×1

1

Hence proved.