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KEAM 2013 Math Paper
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© examsnet.com
Question : 93
Total: 120
If
f
(
x
)
=
c
o
s
−
1
(
2
c
o
s
x
+
3
s
i
n
x
√
13
)
,
then
[
f
′
(
x
)
]
2
is equal to
√
1
+
x
1
+
2
x
2
1
0
Validate
Solution:
Given,
f
(
x
)
=
cos
−
1
{
2
cos
x
+
3
sin
x
√
13
}
=
cos
−
1
{
2
√
13
cos
x
+
3
√
13
sin
x
}
=
cos
−
1
(
cos
α
cos
x
+
sin
α
⋅
sin
x
)
=
cos
−
1
cos
(
α
+
x
)
=
α
+
x
On, differentiating w.r.t.
x
, we get
f
′
(
x
)
=
1
⇒
[
f
′
(
x
)
]
2
=
1
© examsnet.com
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