Question

Show that
Tan 48° tan 23° tan 42° tan 67°=1​

Answer 1

QUESTION ⤵️

Show that

Tan 48° tan 23° tan 42° tan 67°=1

ANSWER ⤵️

{we know that 48+42=90,

hence, 42=90-48

similarly, 23+67=90,

hence, 67=90-23}

{ tan(90-theta)=cot theta}

and

{cot theta=1/tan theta}

Taking LHS

tan48° tan(90-48) tan23° tan(90-23)

tan48° cot48° tan23° cot23°

(tan48°× 1/tan48° ) ( tan23°× 1/tan 23°)

1×1

=1

=RHS

$\huge\mathfrak\smile\pink{hope \: it \: helps}\smile$