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Byju's Answer
Standard XI
Mathematics
Solving Simultaneous Trigonometric Equations
Let λ and ...
Question
Let
λ
and
α
be real. Find the set of all values of
λ
for which the system of linear equations
λ
x
+
(
sin
α
)
y
+
(
cos
α
)
z
=
0
,
x
+
(
cos
α
)
y
+
(
sin
α
)
z
=
0
and
−
x
+
(
sin
α
)
y
−
(
cos
α
)
z
=
0
Has a non-trivial solution. For
λ
=
1
, find all values of
α
Open in App
Solution
For non-trivial solution
∣
∣ ∣
∣
λ
sin
α
cos
α
1
cos
α
sin
α
−
1
sin
α
−
cos
α
∣
∣ ∣
∣
=
0
λ
(
−
cos
2
α
−
sin
2
α
)
−
sin
α
(
sin
α
−
cos
α
)
+
cos
α
(
sin
α
+
cos
α
)
=
0
.
−
λ
(
sin
2
α
+
cos
2
α
)
−
sin
2
α
+
cos
2
α
−
sin
α
cos
α
+
sin
α
cos
α
=
0.
λ
=
cos
2
α
−
sin
2
α
λ
=
cos
2
α
λ
can be form
[
−
1
,
1
]
because range of
cos
2
α
is form
[
−
1
,
1
]
.
For
λ
=
1
cos
2
α
=
1
α
=
n
π
. where
n
is an integer.
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0
Similar questions
Q.
Let
λ
and
α
be real. Let
S
denote the set of all values of
λ
for which the system of linear equations
λ
x
+
(
sin
α
)
y
+
(
cos
α
)
z
=
0
x
+
(
cos
α
)
y
+
(
sin
α
)
z
=
0
−
x
+
(
sin
α
)
y
−
(
cos
α
)
z
=
0
has a non-trivial solution then
S
contains
Q.
Let
λ
and
α
be real. Find the set of all values of
λ
for which the system of linear equation
λ
x
+
(
s
i
n
α
)
y
+
(
c
o
s
α
)
z
=
0
x
+
(
c
o
s
α
)
y
+
(
s
i
n
α
)
z
=
0
−
x
+
(
s
i
n
α
)
y
−
(
c
o
s
α
)
z
=
0
has a non-trivial solution. For
λ
=
1
, find all values of
α
Q.
Let S denote the set of all values of
λ
for which the system of linear equations
λ
x
+
(
sin
α
)
y
+
(
cos
α
)
z
=
0
,
x
+
(
cos
α
)
y
+
(
sin
α
)
z
=
0
,
−
x
+
(
sin
α
)
y
−
(
cos
α
)
z
=
0
,
has a non-trivial solution
∀
α
∈
R
, then S contains
Q.
Let
λ
and
α
be real. Find the set of all values of
λ
for which the system of linear equations
λ
x
+
(
s
i
n
α
)
y
+
(
c
o
s
α
)
z
=
0
x
+
(
c
o
s
α
)
y
+
(
s
i
n
α
)
z
=
0
−
x
+
(
s
i
n
α
)
y
+
(
c
o
s
α
)
z
=
0
has a non-trivial solution. For
λ
=
1
, find all values of
α
which are possible
Q.
Let
λ
and
α
be real. The set of all values of
λ
for which the system of linear equations
λ
x
+
(
sin
α
)
y
+
(
cos
α
)
z
=
0
x
+
(
sin
α
)
y
−
(
cos
α
)
z
=
0
−
x
+
(
sin
α
)
y
+
(
cos
α
)
z
=
0
has a non-trivial solution is
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