Question

tan 48° tan 16° tan 42° tan 74=
​

Answer 1

We know that,

• tan (90°- θ) = cot θ
• tan θ = 1 / cot θ

Therefore,

• tan 48° = tan (90 - 42)° = cot 42°

• tan 74° = tan (90 - 16)° = cot 16°

• tan 42° = tan (90 - 48)°= cot 48°

• tan 16° = tan (90 - 74)° = cot 74°

Therefore,

=tan 48°×tan 16°×tan 42°×tan 74°

=tan 48°×tan 42°×tan 16° × tan 74°

=tan 48°×cot 48° × tan 16° × cot 16

=$tan 48° \times \frac{1}{tan48°} \times tan16° \times \frac{1}{tan16°}$

= 1

Therefore,

tan 48° tan 16° tan 42° tan 74° = 1

$\boxed{@\:\:Raj}$