Question

tan 48° tan 23° tan 42° tan 67° = 1​

Answer 1

Question :

Prove : tan 48° tan 23° tan 42° tan 67° = 1

Solution :

$: \tan(48) \tan(23) \tan(42) \tan(67)$

$\implies \: \tan(48) \tan(23) \tan(90 - 48) \tan(90 - 23)$

$\implies \: \tan(48) \tan(23) \cot(48) \cot(23)$

$\implies \: ( \tan(48) \times \cot(48) )( \tan(23) \cot(23) )$

$\implies \: 1 \times 1$

$\implies1$

Hence , proved that

• tan 48° tan 23° tan 42° tan 67° = 1

Formulae used :

• tan(90 - ∅) = cot ∅

• tan ∅ × cot ∅ = 1

Answer 2

tan (48) tan 23 tan 42 tan 67

tan48 tan23 tan90-48 t a n 90 - 23

t a n 48 tan23 cot48cot23

tan48 cot48 tan23 c o t 23

1X1

1