Question

the value of (tan7°×tan 44°×tan46°×tan83°)is​

Answer 1

tan7 × tan 44 × tan 46 × tan 83 = 1

Answer 2

Answer:

$\tan 7^\circ\times \tan 44^\circ\times \tan46^\circ\times \tan 83^\circ=1$

Step-by-step explanation:

Given : Expression $\tan 7^\circ\times \tan 44^\circ\times \tan46^\circ\times \tan 83^\circ$

To find : The value of the expression ?

Solution :

Expression $\tan 7^\circ\times \tan 44^\circ\times \tan46^\circ\times \tan 83^\circ$

We can write, $\tan83^\circ=\tan(90-7)^\circ$ and $\tan46^\circ=\tan(90-44)^\circ$

$=\tan 7^\circ\times \tan 44^\circ\times\tan(90-44)^\circ\times \tan(90-7)^\circ$

Substitute, $\tan(90-7)^\circ=\cot 7^\circ$ and $\tan(90-44)^\circ=\cot 44^\circ$

$=\tan 7^\circ\times \tan 44^\circ\times\cot 44^\circ\times \cot 7^\circ$

We know that, $\cot\theta=\frac{1}{\tan\theta}$

$=\tan 7^\circ\times \tan 44^\circ\times\frac{1}{\tan44^\circ}\times \frac{1}{\tan7^\circ}$

Cancel the like terms,

$=1\times 1$

$=1$

Therefore, $\tan 7^\circ\times \tan 44^\circ\times \tan46^\circ\times \tan 83^\circ=1$