Show that:

tan 48° tan 23° tan 42° tan 67° = 1

jsshudhwuhujwnijsdiw

Dear Student

tan 48° tan 23° tan 42° tan 67°
Simplify the given problem
by converting some of the tan functions to the cot functions
We know that,
tan 48° = tan (90° - 42°)
= cot 42°
tan 23° = tan (90° - 67°)
= cot 67°

= tan (90° - 42°) tan (90° - 67°) tan 42° tan 67°
Substitute the values
= cot 42° cot 67° tan 42° tan 67°
= (cot 42° tan 42°) (cot 67° tan 67°)
= 1×1
= 1

Thanks