If sin60°+sin70° =2sinA cosB, find A and B
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If sin60°+sin70° =2sinA cosB, find A and B
answer fast and correctly please
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Answer:
Let
sin
70
⋅
sin
50
−
cos
85
⋅
cos
65
=
I
Using
2
sin
A
sin
B
=
cos
(
A
+
B
)
−
cos
(
A
−
B
)
2
cos
A
cos
B
=
cos
(
A
−
B
)
+
cos
(
A
+
B
)
We get,
I
=
1
2
(
cos
20
−
cos
120
−
cos
150
−
cos
20
)
=
1
2
(
−
cos
120
−
cos
150
)
=
1
2
(
sin
30
+
sin
60
)
=
1
2
(
1
2
+
√
3
2
)
=
√
3
+
1
4