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Byju's Answer
Standard XII
Mathematics
General Solution of Trigonometric Equation
Let α=a+1a ...
Question
Let
cot
α
=
a
+
1
a
and
cot
β
=
2
a
+
1
then find the acute value of
α
+
β
.
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Solution
Given,
cot
α
=
a
+
1
a
......(1) and
cot
β
=
2
a
+
1
......(2).
Now,
cot
(
α
+
β
)
=
cot
α
.
cot
β
−
1
cot
β
+
cot
α
=
(
a
+
1
)
(
2
a
+
1
)
a
−
1
a
+
1
a
+
2
a
+
1
[ Using (1) and (2)]
=
2
a
2
+
2
a
+
1
2
a
2
+
2
a
+
1
=
1
.
So
cot
(
α
+
β
)
=
1
or,
α
+
β
=
π
4
. [ Taking acute angle]
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Similar questions
Q.
Let
α
,
β
are acute and
tan
α
=
a
a
+
1
,
tan
β
=
1
2
a
+
1
, then find the value of
α
+
β
.
Q.
If each of
α
,
β
,
γ
is a positive acute angle such that
sin
(
α
+
β
−
γ
)
=
1
2
,
cos
(
β
+
γ
−
α
)
=
1
2
and
tan
(
γ
+
α
−
β
)
=
1
, find the value of
α
,
β
,
γ
.
Q.
If
(
α
+
1
)
(
β
−
1
)
+
(
β
+
1
)
(
α
−
1
)
α
+
(
α
−
1
)
(
β
−
1
)
=
0
and
α
(
α
+
1
)
(
β
+
1
)
−
(
α
−
1
)
(
β
−
1
)
=
0
Also let
A
=
{
α
+
1
α
−
1
,
β
+
1
β
−
1
}
and
B
=
{
2
α
α
−
1
,
2
β
β
+
1
}
If
A
∩
B
≠
ϕ
, then find all the permissible value of parameter
"
a
"
.
Q.
Let
α
and
β
are complex numbers satisfying
|
α
+
1
+
i
|
=
1
and
|
β
−
2
−
3
i
|
=
6
such that
6
|
α
|
m
a
x
−
|
β
|
m
a
x
=
√
a
−
√
b
;
a
,
b
∈
R
+
then the value of
√
b
2
−
2
a
is
Q.
If
α
,
β
are acute angles such that
(
α
+
β
)
and
(
α
−
β
)
satisfy the equation
tan
2
θ
−
4
tan
θ
+
1
=
0
,
then:
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