Tan A = 1/5 and tan B = 1/4 Find tan 2 (A-B)

Question

asked Feb 28, 2022 55.8k views

1 Answer

Junkdog · Answer 1 · 2022-03-07T02:41:22+0000

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
.