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KEAM 2019 Math Paper
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© examsnet.com
Question : 4
Total: 121
If
f
(
x
)
=
sin
log
x
, then value of
f
(
x
y
)
+
f
(
x
y
)
−
2
f
(
x
)
cos
log
y
is equal to
0
cos
log
x
x
1
1
2
None of these
Validate
Solution:
(a)
f
(
x
y
)
=
sin
log
x
y
=
sin
(
log
x
+
log
y
)
.
.
.
(
i
)
f
(
x
y
)
=
sin
log
(
x
y
)
=
sin
(
log
x
−
log
y
)
.
.
.
(
i
i
)
On adding Eqs. (i) and (ii)
f
(
x
y
)
+
f
(
x
∕
y
)
=
2
sin
log
x
cos
log
y
∴
f
(
x
y
)
+
f
(
x
y
)
=
2
f
(
x
)
cos
log
y
⇒
f
(
x
y
)
+
f
(
x
∕
y
)
−
2
f
(
x
)
cos
log
y
=
0
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