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IIT JEE Advanced 2010 Paper 1
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© examsnet.com
Question : 78
Total: 84
The number of values of θ in the interval
(
−
π
2
,
π
/
)
such that θ ≠
n
π
5
for n = 0, ±1, ± 2 and tanθ = cot5θ as well as sin 2θ = cos4θ is _____.
Your Answer:
Validate
Solution:
We have tanθ = cot5θ.
⇒ cos 6θ = 0
4
c
o
s
3
2
θ
−
3
c
o
s
2
θ
=
0
⇒ cos 2θ = 0 or ±
√
3
2
sin 2θ = cos 4θ
⇒
2
s
i
n
2
2
θ
+
s
i
n
2
θ
−
1
=
0
2
s
i
n
2
2
θ
+
2
s
i
n
2
θ
−
s
i
n
2
θ
−
1
=
0
sin 2θ = - 1 or sin 2θ =
1
2
cos 2θ = 0 and sin 2θ = - 1
cos 2θ = ±
√
3
2
, sin 2θ =
1
2
⇒ 2θ =
π
6
,
5
π
6
⇒ θ =
π
12
,
5
π
12
Therefore,
θ =
−
π
4
,
π
12
,
5
π
12
© examsnet.com
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