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

Find tan 2 (A-B) ​

User Jobsamuel
by
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1 Answer

14 votes

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).

User Junkdog
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4.0k points