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Question
Mathematics
If the solution of the equation log cos x cot x+4 log sin x tan x=1, x ∈(0, (π/2)), is sin -1((α+√β/2)), where α, β are integers, then α+β is equal to :
Q. If the solution of the equation
lo
g
c
o
s
x
cot
x
+
4
lo
g
s
i
n
x
tan
x
=
1
,
x
∈
(
0
,
2
π
)
, is
sin
−
1
(
2
α
+
β
)
, where
α
,
β
are integers, then
α
+
β
is equal to :
7403
139
JEE Main
JEE Main 2023
Trigonometric Functions
Report Error
A
6
0%
B
4
100%
C
5
0%
D
3
0%
Solution:
lo
g
c
o
s
x
cot
x
+
4
lo
g
s
i
n
x
tan
x
=
1
⇒
l
n
c
o
s
x
l
n
c
o
s
x
−
l
n
s
i
n
x
+
4
l
n
s
i
n
x
l
n
s
i
n
x
−
l
n
c
o
s
x
=
1
⇒
(
ln
sin
x
)
2
−
4
(
ln
sin
x
)
(
ln
cos
x
)
+
4
(
ln
cos
x
)
2
=
1
⇒
ln
sin
x
=
2
ln
cos
x
⇒
sin
2
x
+
sin
x
−
1
=
0
⇒
sin
x
=
2
−
1
+
5
∴
α
+
β
=
4
Correct option (4)