Question

show that: tan 48° tan 23° tan 42° tan 67° = 1​

Answer 1

as we know tan ( 90°- theta ) = cot theta

so

tan (90°-42°)tan(90°-67°) tan42° tan67°=1

cot42° cot67° tan42° tan67°=1

cot 42° tan 42° cot 67° tan 67° = 1

now we also kow cot theta= 1/ tan theta

so

1/ tan 42° × tan42° × 1/ tan 67° × tan 67°=1

1=1

LHS=RHS

I HOPE THIS WILL HELP