Question

Tan A = 1/5 and tan B = 1/4

Find tan 2 (A-B) ​

Answer 1

Given:

`\tan A=(1)/(5)`

`\tan B=(1)/(4)`

To find:

The value of
`\tan^2(A-B)`.

Solution:

We know that,

`\tan (A-B)=(\tan A-\tan B)/(1+\tan A\tan B)`

Putting the given values, we get

`\tan (A-B)=((1)/(5)-(1)/(4))/(1+(1)/(5)\cdot (1)/(4))`

`\tan (A-B)=((4-5)/(20))/(1+(1)/(20))`

`\tan (A-B)=((-1)/(20))/((20+1)/(20))`

`\tan (A-B)=(-1)/(21)`

Taking square on both sides, we get

`\tan^2 (A-B)=\left( (-1)/(21)\right)^2`

`\tan^2 (A-B)=(1)/(441)`

Therefore, the value of
`\tan^2(A-B)` is
`(1)/(441)`.