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Byju's Answer
Standard XII
Mathematics
Domain and Range of Basic Inverse Trigonometric Functions
Eliminate θ...
Question
Eliminate
θ
from the equations
tan
(
n
θ
+
α
)
−
tan
(
n
θ
+
β
)
=
x
and
cot
(
n
θ
+
α
)
−
cot
(
n
θ
+
β
)
=
y
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Solution
cot
(
n
θ
+
α
)
−
cot
(
n
θ
+
β
)
=
y
⇒
1
tan
(
n
θ
+
α
)
−
1
tan
(
n
θ
+
β
)
=
y
⇒
tan
(
n
θ
+
β
)
−
tan
(
n
θ
+
α
)
tan
(
n
θ
+
α
)
tan
(
n
θ
+
β
)
=
y
⇒
−
x
y
=
tan
(
n
θ
+
α
)
tan
(
n
θ
+
β
)
∴
tan
(
n
θ
+
α
)
−
(
n
θ
+
β
)
=
tan
(
n
θ
+
α
)
−
tan
(
n
θ
+
β
)
1
+
tan
(
n
θ
+
α
)
tan
(
n
θ
+
β
)
=
x
1
−
x
y
=
x
y
y
−
x
⇒
tan
(
α
+
β
)
=
x
y
y
−
x
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0
Similar questions
Q.
If
m
cos
(
θ
+
α
)
=
n
cos
(
θ
−
α
)
, show that
(
m
−
n
)
cot
θ
=
(
m
+
n
)
tan
α
Q.
The number of
α
-particles scattered per unit area
N
(
θ
)
at scattering angle
θ
varies inversely as
Q.
If cos
(
θ
−
α
)
= x and sin
(
θ
−
β
)
= y, then prove that
c
o
s
2
(
α
−
β
)
+
2
x
y
s
i
n
(
α
−
β
)
=
x
2
+
y
2
Q.
If
α
,
β
,
γ
are roots of equation
x
3
−
x
−
1
=
0
, then the equation whose roots are
1
β
+
γ
,
1
γ
+
α
,
1
α
+
β
is -
Q.
Assertion :If
x
tan
(
θ
+
α
)
=
y
tan
(
θ
+
β
)
=
z
tan
(
θ
+
γ
)
, then
∑
x
+
y
x
−
y
sin
2
(
α
−
β
)
=
0
Reason:
x
+
y
x
−
y
=
tan
(
θ
+
α
)
+
tan
(
θ
+
β
)
tan
(
θ
+
α
)
−
tan
(
θ
+
β
)
=
sin
(
2
θ
+
α
+
β
)
sin
(
α
+
β
)
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