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Byju's Answer
Standard XII
Mathematics
Solving Simultaneous Trigonometric Equations
The smallest ...
Question
The smallest positive value of
x
which satisfies the equation
log
cos
x
sin
x
+
log
sin
x
cos
x
=
2
is
A
π
2
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B
π
3
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C
π
4
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D
π
6
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Solution
The correct option is
C
π
4
log
cos
x
sin
x
+
log
sin
x
cos
x
=
2
Let
log
cos
x
sin
x
=
t
⇒
t
+
1
t
=
2
⇒
t
2
−
2
t
+
1
=
0
⇒
(
t
−
1
)
2
=
0
⇒
t
=
1
⇒
log
cos
x
sin
x
=
1
or
sin
x
=
cos
x
⇒
tan
x
=
1
⇒
x
=
π
4
Suggest Corrections
4
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