If a
1
, a
2
,....,a
n
are in AP with common difference d, then the sum of the series sind(csca
1
csca
2
+csca
2
csca
3
+...+csca
n−1
csca
n
) is
Answers
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2
Answer: ANSWER
Given
a
1
,a
2
,a
3
.....an be A.P with d as common difference, then
d=a
2
−a
1
=a
3
−a
2
.........=a
n
−a
n−1
sind[csca
1
csca
2
+csca
2
csc2
3
+....+csca
n−1
csca
n
]
=
sina
1
sina
2
sind
+
sina
2
sina
3
sind
....+
sina
n−1
sina
n
sind
=
sina
1
sina
2
sin(a
2
−a
1
)
+
sina
2
sina
3
sin(a
3
−a
2
)
....+
sina
n−1
sina
n
sin(a
n
−a
n−1
)
=
sina
1
sina
2
sina
1
cosa
2
−cosa
1
sina
2
+
sina
2
sina
3
sina
2
cosa
3
−cosa
2
sina
3
....+
sina
n−1
sina
n
sina
n
cosa
n−1
−cosa
n−1
sina
n
=cota
1
−cota
2
+cota
2
−cota
3
+.....+cota
n−1
−cota
n
Step-by-step explanation:
dhinchak40:
thx
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