if theta is the angel between the lines x/a+y/b=1, x/b+y/a=1 then find the value of sin theta( a>b)
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Answer:
Given
a
x
+
b
y
=1 …………(1)
a
x
−
b
y
=1 ………….(2)
Equation (1) can be written as
y=−
a
b
x+1
where slope [m
1
=
a
−b
]
Equation (2) can be written as
y=
a
b
x−1
where slope [m
2
=
a
b
]
now angle between line (1) & (2) is
tanθ=
∣
∣
∣
∣
∣
1+m
1
m
2
m
1
−m
2
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
∣
∣
∣
1−
a
2
b
2
a
−b
−
a
b
∣
∣
∣
∣
∣
∣
∣
∣
tanθ=
∣
∣
∣
∣
∣
∣
∣
∣
a
2
a
2
−b
2
−
a
2b
∣
∣
∣
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
a
2
−b
2
−2ba
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
−b
2
+a
2
−2ab
∣
∣
∣
∣
∣
Hence tangent of an angle between line (1) & (2)
is
a
2
−b
2
2ab
.
Step-by-step explanation:
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