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03/02/2022 7:01 pm
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cosec 18° is a root of the equation
(1) x2 + 2x – 4 = 0
(2) 4x2 + 2x – 1 = 0
(3) x2 – 2x + 4 = 0
(4) x2 – 2x – 4 = 0
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03/02/2022 7:05 pm
Correct answer: (4) x2 – 2x – 4 = 0
Explanation:
cosec 18° = \(\frac{1}{sin 18°}\)
= \(\frac{4}{\sqrt 5 - 1}\) = \(\sqrt 5 + 1\)
Let cosec 18° = x = \(\sqrt 5 + 1\)
⇒ x - 1 = √5
Squaring both sides, we get
x2 - 2x + 1 = 5
⇒ x2 – 2x – 4 = 0