Please solve this:
If tan
−1
x−4
x−3
+tan
−1
x+4
x+3
=
4
3
, then find the value of x
Answers
Answered by
1
Answer:
x
2
=
2−2tan(
4
3
)
24−25tan(
4
3
)
Step-by-step explanation:
Given tan
−1
(
x−4
x−3
)+tan
−1
(
x+4
x+3
)=
4
3
Let tan
−1
(
x−4
x−3
)=a and tan
−1
(
x+4
x+3
)=b
So we have
x−4
x−3
=tana and
x+4
x+3
=tanb
The given equation will become a+b=
4
3
, Now apply tan on both sides
We get tan(a+b)=
1−tana×tanb
tana+tanb
=tan(
4
3
)
By substituting tan a and tanb values , we get
1−
x−4
x−3
×
x+4
x+3
x−4
x−3
+
x+4
x+3
=
(x−4)(x+4)+(x−3)(x+3)
(x−3)(x+4)+(x+3)(x−4)
=
2x
2
−25
2x
2
−24
=tan(
4
3
)
By solving , we get x
2
=
2−2tan(
4
3
)
24−25tan(
4
3
)
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