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UPSEE 2019 Solved Paper
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© examsnet.com
Question : 143
Total: 150
The sum of all solutions of the equation
cos
3
θ
=
sin
2
θ
in the interval
[
−
π
2
,
π
2
]
is
−
π
5
−
π
3
π
4
3
π
10
Validate
Solution:
We have,
cos
3
θ
=
sin
2
θ
⇒
4
cos
3
θ
−
3
cos
θ
=
2
sin
θ
cos
θ
⇒
4
cos
2
θ
−
3
=
2
sin
θ
or
cos
θ
=
0
⇒
4
(
1
−
sin
2
θ
)
−
3
=
2
sin
θ
or
θ
=
π
2
,
−
π
2
Now,
4
sin
2
θ
+
2
sin
θ
−
1
=
0
⇒
sin
θ
=
−
2
±
√
20
8
⇒
sin
θ
=
−
1
±
√
5
4
⇒
sin
θ
=
√
5
−
1
4
and
sin
θ
=
−
(
√
5
+
1
)
4
θ
1
=
π
10
and
θ
2
=
−
3
π
10
⇒
θ
1
+
θ
2
=
π
10
−
3
π
10
=
−
π
5
© examsnet.com
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