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Standard XII
Mathematics
Sin(A+B)Sin(A-B)
Question
If
(
tan
A
−
tan
B
)
=
x
and
(
cot
B
−
cot
A
)
=
y
, then
cot
(
A
−
B
)
is
1
x
+
1
y
1
x
−
y
1
x
+
y
1
x
−
1
y
1
x
+
y
A
1
x
+
y
B
1
x
−
1
y
C
1
x
+
1
y
D
1
x
−
y
E
1
x
+
y
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Solution
Verified by Toppr
Given
tan
A
−
tan
B
=
x
.
.
.
(
i
)
and
cot
B
−
cot
A
=
y
.
.
.
(
i
i
)
From Eq(ii)
cot
B
−
cot
A
=
y
we get
⇒
1
tan
B
−
1
tan
A
=
y
⇒
tan
A
−
tan
B
tan
B
tan
A
=
y
⇒
x
tan
B
tan
A
=
y
∴
cot
(
A
−
B
)
=
cot
A
cot
B
+
1
cot
B
−
cot
A
=
y
x
+
1
y
............... (Eq(ii) and Eq(iii)
=
1
x
+
1
y
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Similar Questions
Q1
If
x
=
tan
A
−
tan
B
,
y
=
cot
B
−
cot
A
then
1
x
+
1
y
=
View Solution
Q2
If
tan
A
−
tan
B
=
x
and
cot
B
−
cot
A
=
y
, where
x
,
y
≠
0
, then
cot
(
A
−
B
)
is
View Solution
Q3
If
tan
A
−
tan
B
=
x
and
cot
B
−
cot
A
=
y
Prove that
cot
(
A
−
B
)
=
1
x
+
1
y
?
View Solution
Q4
If
tan
A
−
tan
B
=
x
,
cot
B
−
cot
A
=
y
, prove that
cot
(
A
−
B
)
=
(
1
x
)
+
(
1
y
)
View Solution
Q5
If
tan
A
=
x
=
sin
B
1
−
x
cos
B
and
tan
B
=
y
sin
A
1
−
y
cos
A
then
sin
A
sin
B
=
View Solution