Question

tan 48° tan 23° tan 42° tan 67° = 1

Answer 1

=tan48 tan23 tan(90-48) tan (90-23)
=tan48 cos48 tan23 cos23
=1*1
=1

Answer 2

Hi...
Here is your answer:

LHS: Tan 48° tan 23° tan 42° tan 67° .....(1)

We know that tanA=cot(90-A)

Tan 48=cot 42
Tan 23= cot 63

Put them in (1)

Cot42 tan42 cot63 tan 63....(2)

We also know that tanA=1/cotA

Tan 42=1/cot42
Tan63=1/cot63

Put in equation 2

=Cot42*(1/cot42)*cot63*(1/cot63)
=1*1

=1

LHS=RHS


Hence prooved

Hope u get your answer!!