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Byju's Answer
Standard XII
Physics
Antiderivative
If A+B+C=π/...
Question
If
A
+
B
+
C
=
π
/
2
, then show that
i.
cot
A
+
cot
B
+
cot
C
=
cot
A
cot
B
cot
C
ii.
tan
A
tan
B
+
tan
B
tan
C
+
tan
C
tan
A
=
1
.
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Solution
A
+
B
+
C
=
π
2
cot
A
+
cot
B
+
cot
C
simplifying in terms of sin and cos
=
cos
A
sin
A
+
cos
B
sin
B
+
cos
C
sin
C
=
(
cos
A
sin
B
sin
c
+
cos
B
sin
A
sin
c
+
cos
C
sin
A
sin
B
)
sin
A
sin
B
sin
C
=
−
cos
(
A
+
B
+
C
)
+
cos
A
cos
B
cos
C
sin
A
sin
B
sin
C
=
cos
A
cos
B
cos
C
sin
a
sin
B
sin
C
=
cot
A
cot
B
cot
C
tan
A
tan
B
+
tan
B
tan
C
+
tan
C
tan
A
simplifying in terms of sin and cos
=
sin
A
cos
A
.
sin
B
cos
B
.
sin
C
cos
C
+
sin
C
cos
C
.
sin
A
cos
A
=
sin
A
sin
B
cos
C
+
sin
B
sin
C
cos
A
+
sin
C
sin
A
cos
B
cos
A
cos
B
cos
C
=
cos
A
cos
B
cos
C
−
cos
(
A
+
B
+
C
)
cos
A
cos
B
cos
C
=
1
Suggest Corrections
0
Similar questions
Q.
If
A
=
35
0
,
B
=
15
0
and
C
=
40
0
, then the value of
tan
A
tan
B
+
tan
B
tan
C
+
tan
C
tan
A
is equal to
Q.
A
+
B
+
C
=
π
2
, then
tan
A
tan
B
+
tan
B
tan
C
+
tan
A
tan
C
=
Q.
If
sin
A
sin
B
sin
C
=
p
and
cos
A
cos
B
cos
C
=
q
, where
A
,
B
,
C
are the angles of a
Δ
A
B
C
, then
tan
A
tan
B
+
tan
B
tan
C
+
tan
C
tan
A
is equal to
Q.
In any
Δ
A
B
C
, if
y
=
tan
A
tan
B
+
tan
B
tan
C
+
tan
C
tan
A
, then
Q.
In a
Δ
A
B
C
, if
cos
A
cos
B
cos
C
=
1
3
, then the value of
tan
A
tan
B
+
tan
B
tan
C
+
tan
C
tan
A
is
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