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consider the following statements 1 if y ln sec x
Question:
Consider the following statements:1. If
y
=
ln
(
sec
x
+
tan
x
)
, then
d
y
d
x
=
sec
x
.2. If
y
=
ln
(
cosec
x
−
cot
x
)
, then
d
y
d
x
=
cosec
x
.Which of the above is / are correct?
MHT CET
Updated On:
Jun 23, 2024
(A) 1 only
(B) 2 only
(C) Both 1 and 2
(D) Neither 1 nor 2
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The Correct Option is
C
Solution and Explanation
Explanation:
Concept:
y
=
ln
x
then
d
y
d
x
=
1
x
y
=
tan
x
then
d
y
d
x
=
sec
2
x
y
=
sec
x
then
d
y
d
x
=
sec
x
⋅
tan
x
y
=
cosec
x
then
d
y
d
x
=
−
cosec
x
⋅
cot
x
y
=
cot
x
then
d
y
d
x
=
−
cosec
2
x
Let,
y
=
ln
(
sec
x
+
tan
x
)
⇒
d
y
d
x
=
1
sec
x
+
tan
x
×
(
sec
x
⋅
tan
x
+
sec
2
x
)
⇒
d
y
d
x
=
sec
x
sec
x
+
tan
x
×
(
tan
x
+
sec
x
)
⇒
d
y
d
x
=
sec
x
Statement (1) is true. Now,
y
=
ln
(
cosec
x
−
cot
x
)
,
⇒
d
y
d
x
=
1
cosec
x
−
cot
x
×
(
−
cosec
x
⋅
cot
x
+
cosec
2
x
)
⇒
d
y
d
x
=
cosec
x
cosec
x
−
cot
x
×
(
cosec
x
.
−
cot
x
)
⇒
d
y
d
x
=
cosec
x
Statement (2) is true.Hence, the correct option is (C).
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