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Tardigrade
Question
Mathematics
If 15 sin 4 α+10 cos 4 α=6, for some α ∈ R, then the value of 27 sec 6 α+8 operatornamecosec6 α is equal to :
Q. If
15
sin
4
α
+
10
cos
4
α
=
6
, for some
α
∈
R
, then the value of
27
sec
6
α
+
8
cosec
6
α
is equal to :
1747
218
JEE Main
JEE Main 2021
Trigonometric Functions
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A
350
15%
B
500
32%
C
400
17%
D
250
36%
Solution:
15
sin
4
α
+
10
cos
4
α
=
6
15
sin
4
α
+
10
cos
4
α
=
6
(
sin
2
α
+
cos
2
α
)
2
(
3
sin
2
α
−
2
cos
2
α
)
2
=
0
tan
2
α
=
3
2
⋅
cot
2
α
=
2
3
⇒
27
sec
6
α
+
8
cosec
6
α
=
27
(
sec
6
α
)
3
+
8
(
cosec
6
α
)
3
=
27
(
1
+
tan
2
α
)
3
+
8
(
1
+
cot
2
α
)
3
=
250