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JEE Advanced 2020 Concept Recapitulation Test 4 Paper 1
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© examsnet.com
Question : 54
Total: 54
Sum of solution of the equation
cos
−
1
x
2
−
1
x
2
+
1
+
tan
−
1
2
x
x
2
−
1
=
2
π
3
is ________
Your Answer:
Validate
Solution:
cos
−
1
1
−
x
2
1
+
x
2
+
tan
−
1
2
x
1
−
x
2
=
π
∕
3
Put
x
=
tan
θ
,
−
π
2
<
θ
<
π
2
cos
−
1
(
cos
2
θ
)
+
tan
−
1
(
tan
2
θ
)
=
π
∕
3
For
−
π
<
2
θ
<
−
π
∕
2
−
2
θ
+
2
θ
+
π
=
π
∕
3
(Not possible)
For
−
π
2
<
2
θ
≤
0
−
2
θ
+
2
θ
=
π
∕
3
(Not possible)
For
0
<
2
θ
<
π
∕
2
2
θ
+
2
θ
=
π
∕
3
θ
=
π
12
x
=
2
−
√
3
For
π
2
<
2
θ
<
π
2
θ
+
2
θ
−
π
=
π
∕
3
⇒
θ
=
π
∕
3
x
=
√
3
sum
=
2
−
√
3
+
√
3
=
2
© examsnet.com
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