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Byju's Answer
Standard XII
Mathematics
Trigonometric Ratios of Compound Angles
Find the valu...
Question
Find the value of
sin
47
°
+
sin
61
°
−
sin
11
°
−
sin
25
°
Open in App
Solution
sin
47
∘
+
sin
61
∘
−
(
sin
11
∘
+
sin
25
∘
)
Using the transformation angle formula
sin
C
+
sin
D
=
2
sin
(
C
+
D
2
)
cos
(
C
−
D
2
)
=
(
2
sin
(
47
+
61
2
)
cos
(
47
−
61
2
)
)
−
(
2
sin
(
11
+
25
2
)
cos
(
11
−
25
2
)
)
=
(
2
sin
(
108
2
)
cos
(
−
14
2
)
)
−
(
2
sin
(
36
2
)
cos
(
−
14
2
)
)
=
(
2
sin
54
∘
cos
−
7
∘
)
−
(
2
sin
18
∘
cos
−
7
∘
)
=
2
cos
7
∘
(
sin
54
∘
−
sin
18
∘
)
using
cos
(
−
θ
)
=
cos
θ
=
2
cos
7
∘
(
2
sin
(
54
−
18
2
)
cos
(
54
+
18
2
)
)
using the transformation angle formula
sin
C
−
sin
D
=
2
sin
(
C
−
D
2
)
cos
(
C
+
D
2
)
=
4
cos
7
∘
sin
18
∘
cos
36
∘
We know that
sin
18
∘
=
√
5
−
1
4
and
cos
36
∘
=
√
5
+
1
4
=
4
cos
7
∘
√
5
−
1
4
×
√
5
+
1
4
=
4
cos
7
∘
4
4
×
4
=
cos
7
∘
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0
Similar questions
Q.
Find the value of
sin
47
∘
+
sin
61
∘
−
sin
11
∘
−
sin
25
∘
Q.
sin 47° + sin 61° − sin 11° − sin 25° is equal to
(a) sin 36°
(b) cos 36°
(c) sin 7°
(d) cos 7°
Q.
The value of
x
∈
(
0
,
90
∘
)
satisfying
c
o
s
x
=
s
i
n
61
∘
+
s
i
n
47
∘
−
s
i
n
25
∘
−
s
i
n
11
∘
, where
sin
18
∘
=
√
5
−
1
4
cos
36
∘
=
√
5
+
1
4
Q.
The value of
(
cos
11
∘
+
sin
11
∘
)
(
cos
11
∘
−
sin
11
∘
)
is:
Q.
The value of
(
cos
11
∘
+
sin
11
∘
)
(
cos
11
∘
−
sin
11
∘
)
is
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