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Byju's Answer
Standard XII
Mathematics
Property 7
If sinθ1+sinθ...
Question
If sin θ
1
+ sin θ
2
+ sin θ
3
= 3, then write the value of cos θ
1
+ cos θ
2
+ cos θ
3
.
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Solution
Sine function can take the maximum value of 1.
If,
sin
θ
1
+
sin
θ
2
+
sin
θ
3
=
3
, then we have:
sin
θ
1
= 1
⇒
θ
1
=
π
2
Similarly,
θ
2
=
θ
3
=
π
2
⇒
cos
θ
1
=
cos
θ
2
=
cos
θ
3
=
0
⇒
cos
θ
1
+
cos
θ
2
+
cos
θ
3
=
0
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0
Similar questions
Q.
If
sin
θ
1
+
sin
θ
2
+
sin
θ
3
=
3
then
cos
θ
1
+
cos
θ
2
+
cos
θ
3
=.................
Q.
If
cos
Θ
1
+
cos
Θ
2
+
cos
Θ
3
=
3
,
find
sin
Θ
1
+
sin
Θ
2
+
sin
Θ
3
.
Q.
Let A and B denote the statements
A:
c
o
s
θ
1
+
c
o
s
θ
2
+
c
o
s
θ
3
=
0
B:
s
i
n
θ
1
+
s
i
n
θ
2
+
s
i
n
θ
3
=
0.
If
c
o
s
(
θ
1
−
θ
2
)
+
c
o
s
(
θ
2
−
θ
3
)
+
c
o
s
(
θ
3
−
θ
1
)
=
−
3
2
Then which one of following is correct ?
Q.
In
Δ
ABC having vertices
A
(
a
c
o
s
θ
1
,
a
s
i
n
θ
1
)
,
B
(
a
c
o
s
θ
2
,
a
s
i
n
θ
2
)
and
C
(
a
c
o
s
θ
3
,
a
s
i
n
θ
3
)
is equilateral, then which of the followings is/are true?
Q.
The vertices of a triangle are
A
(
x
1
,
x
1
tan
θ
1
)
,
B
(
x
2
,
x
2
tan
θ
2
)
&
C
(
x
3
,
x
3
tan
θ
3
)
If the circumcentre of the triangle ABC is at the origin &
H
(
¯
¯
¯
x
,
¯
¯
¯
y
)
be its orthocentre, then
¯
¯
¯
x
¯
¯
¯
y
=
cos
θ
1
+
cos
θ
2
+
cos
θ
3
sin
θ
1
+
sin
θ
2
+
sin
θ
3
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