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Byju's Answer
Standard XII
Mathematics
Geometric Interpretation of Def.Int as Limit of Sum
If 0<x<π2 a...
Question
If
0
<
x
<
π
2
and
cos
x
=
3
√
10
, then the value of
log
10
sin
x
+
log
10
cos
x
+
log
10
tan
x
is equal to
A
0
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B
1
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C
−
1
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D
none of these
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Solution
The correct option is
C
−
1
Given that,
0
<
x
<
π
2
and
cos
x
=
3
√
10
Let,
a
=
log
10
sin
x
+
log
10
cos
x
+
log
10
tan
x
⇒
a
=
log
10
(
sin
x
cos
x
tan
x
)
[
∵
log
a
+
log
b
+
log
c
=
log
(
a
b
c
)
]
=
log
10
sin
2
x
=
log
10
(
1
−
cos
2
x
)
⇒
a
=
log
10
⎛
⎝
1
−
(
3
√
10
)
2
⎞
⎠
=
log
10
10
−
1
=
−
1
log
10
10
=
−
1
,
[
∵
log
a
a
=
1
]
Ans: C
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0
Similar questions
Q.
Find
x
, if
log
10
(
x
+
1
)
+
log
10
(
x
−
1
)
=
log
10
11
+
2
log
10
3
Q.
If
x
+
log
10
(
1
+
2
x
)
=
x
log
10
5
+
log
10
6
, then the value of
x
is
Q.
If
y
=
log
10
x
+
log
x
10
+
log
x
x
+
log
10
10
, then
d
y
d
x
is equal to
Q.
If
log
10
2
=
0.3010
and
log
10
3
=
0.4771
, then find the approximate value of
log
10
192
Q.
If
log
10
(
x
3
+
y
3
)
−
log
10
(
x
2
+
y
2
−
x
y
)
≤
2
, then the maximum value of
x
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, for all
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≥
0
,
y
≥
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, is
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