Question

Show tan48 tan16 tan42 tan74=1

Answer 1

tan 48 tan 16 tan 42 tan 74=1

LHS = cot(90-48). tan 16. tan 42 . cot(90-74)
= cot 42. tan 16. tan 42 . tan 16
= cot 42. tan 42. cot 16 . tan 16
= 1× 1
= 1

LHS=RHS

Answer 2

Step-by-step explanation:

Since we have given that

$\tan 48\tan 16\tan 42\tan 74$

We need to prove the above expression is equal to 1.

As we know that

$\tan(90^\circ-\theta)=\cot \theta\\\\and\\\\\tan \theta \cot\theta=1$

so, we can rewrite it as :

$\tan 48\tan 42\tan 16\tan 74\\\\=\tan(90-42)\tan 42\tan(90-74)\tan74\\\\=\cot48\tan 42\cot 74\tan 74\\\\=1\times 1\\\\=1$

Hence, proved.