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Standard XII
Maths
Question
If
tan
A
−
tan
B
=
x
,
cot
B
−
cot
A
=
y
, prove that
cot
(
A
−
B
)
=
(
1
x
)
+
(
1
y
)
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Solution
Verified by Toppr
⇒
cot
B
−
cot
A
=
y
∴
1
(
tan
B
)
−
1
(
tan
A
)
=
y
⇒
tan
A
−
tan
B
tan
A
tan
B
=
y
⇒
x
y
=
tan
A
tan
B
Now
cot
(
A
−
B
)
=
1
tan
(
A
−
B
)
=
1
+
tan
A
tan
B
tan
A
−
tan
B
=
1
+
x
y
x
=
1
x
+
1
y
Hence Proved.
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11
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If
tan
A
−
tan
B
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,
cot
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−
cot
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=
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, prove that
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A
−
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)
=
(
1
x
)
+
(
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)
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