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Byju's Answer
Standard XII
Mathematics
Solution of Triangle
If y = √tan...
Question
If
y
=
√
tan
x
+
√
tan
x
+
√
tan
x
+
⋯
to
∞
, then
d
y
d
x
=
p
sec
2
x
q
y
+
r
,
p
,
q
,
r
∈
N
. Find the minimum positive value of
p
+
q
+
r
.
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Solution
Square both sides the given equation,
⇒
y
2
=
tan
x
+
y
Now differentiate both sides with respect to
x
⇒
2
y
d
y
d
x
=
sec
2
x
+
d
y
d
x
⇒
(
2
y
−
1
)
d
y
d
x
=
sec
2
x
∴
d
y
d
x
=
sec
2
x
2
y
−
1
So,
p
=
1
,
q
=
2
,
r
=
−
1
∴
p
+
q
+
r
=
2
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