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Byju's Answer
Standard XII
Mathematics
Domain and Range of Basic Inverse Trigonometric Functions
Prove that: ...
Question
Prove that:
tan
−
1
a
+
cot
−
1
(
a
+
1
)
=
tan
−
1
(
a
2
+
a
+
1
)
.
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Solution
Since
cot
x
=
1
tan
x
,
⇒
cot
−
1
x
=
tan
−
1
1
x
So, we have,
tan
−
1
a
+
cot
−
1
(
a
+
1
)
=
tan
−
1
a
+
tan
−
1
1
a
+
1
=
tan
−
1
(
a
+
1
a
+
1
1
−
a
a
+
1
)
=
tan
−
1
(
a
2
+
a
+
1
)
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0
Similar questions
Q.
Prove that:
1+tan(A)tan(A/2) = tan(A)cot(A/2)-1 = sec(A)
Q.
Inverse circular functions,Principal values of
sin
−
1
x
,
c
o
s
−
1
x
,
tan
−
1
x
.
tan
−
1
x
+
tan
−
1
y
=
tan
−
1
x
+
y
1
−
x
y
,
x
y
<
1
π
+
tan
−
1
x
+
y
1
−
x
y
,
x
y
>
1
.
(a) If
sin
−
1
2
p
1
+
p
2
−
cos
−
1
1
−
q
2
1
+
q
2
=
tan
−
1
2
x
1
−
x
2
then prove that
x
=
p
−
q
1
+
p
q
.
(b) Solve for x
sin
−
1
2
a
1
+
a
2
+
sin
−
1
2
b
1
+
b
2
=
2
tan
−
1
x
(c) Prove that
tan
[
1
2
sin
−
1
2
a
1
+
a
2
+
1
2
cos
−
1
1
−
a
2
1
+
a
2
]
=
2
a
1
−
a
2
.
Q.
Prove that
tan
A
(
1
-
cot
A
)
+
cot
A
(
1
-
tan
A
)
=
(
1
+
tan
A
+
cot
A
)
.
Q.
Prove that:
1
−
tan
A
1
+
tan
A
=
cot
A
−
1
cot
A
+
1
.
Q.
Prove that
(
sec
A
+
tan
A
−
1
)
(
sec
A
−
tan
A
+
1
)
=
2
tan
A
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