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JEE Main Math Class 12 Inverse Trigonometric Functions Questions
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© examsnet.com
Question : 69
Total: 74
If
sin
−
1
(
x
5
)
+
cosec
−
1
(
5
4
)
=
π
2
,
then the values of
x
is
[2007]
4
5
1
3
Validate
Solution:
sin
−
1
(
x
5
)
+
cosec
−
1
(
5
4
)
=
π
2
⇒
sin
−
1
(
x
5
)
=
π
2
−
cosec
−
1
(
5
4
)
⇒
sin
−
1
(
x
5
)
=
π
2
−
sin
−
1
(
4
5
)
[
∵
sin
−
1
x
+
cos
−
1
x
=
π
∕
2
]
⇒
sin
−
1
(
x
5
)
=
cos
−
1
(
4
5
)
sin
−
1
x
5
=
sin
−
1
√
1
−
(
4
5
)
2
[
∵
cos
−
1
x
=
sin
−
1
√
1
−
x
2
]
⇒
sin
−
1
x
5
=
sin
−
1
3
5
⇒
x
5
=
3
5
⇒
x
=
3
© examsnet.com
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