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Joint Entrance Examination
Mathematics
Trigonometric Ratios and Identities
Question 206
Question 206 of 298
Medium
MCQ
cosec
18
∘
\text{cosec}\,18^\circ
cosec
1
8
∘
is a root of the equation:
A
x
2
+
2
x
−
4
=
0
x^2+2x-4=0
x
2
+
2
x
−
4
=
0
B
4
x
2
+
2
x
−
1
=
0
4x^2+2x-1=0
4
x
2
+
2
x
−
1
=
0
C
x
2
−
2
x
+
4
=
0
x^2-2x+4=0
x
2
−
2
x
+
4
=
0
D
x
2
−
2
x
−
4
=
0
x^2-2x-4=0
x
2
−
2
x
−
4
=
0
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Solutions · 1
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Official solution
\[\csc18^\circ = \frac1{\sin18^\circ} = \frac4{\sqrt{5}-1} = \sqrt{5}+1\] Let
x
=
5
+
1
x=\sqrt{5}+1
x
=
5
+
1
. Then
(
x
−
1
)
2
=
5
⟹
x
2
−
2
x
+
1
=
5
⟹
x
2
−
2
x
−
4
=
0
(x-1)^2=5 \implies x^2-2x+1=5 \implies x^2-2x-4=0
(
x
−
1
)
2
=
5
⟹
x
2
−
2
x
+
1
=
5
⟹
x
2
−
2
x
−
4
=
0
.
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