JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
\(\operatorname{cosec} 18^{\circ}\) is a root of the equation :
- A \(x^{2}+2 x-4=0\)
- B \(4 x^{2}+2 x-1=0\)
- C \(x^{2}-2 x+4=0\)
- D \(x^{2}-2 x-4=0\)
Answer & Solution
Correct Answer
(D) \(x^{2}-2 x-4=0\)
Step-by-step Solution
Detailed explanation
\(\operatorname{cosec} 18^{\circ}=\frac{1}{\sin 18^{\circ}}=\frac{4}{\sqrt{5}-1}=\sqrt{5}+1\) Let \(\operatorname{cosec} 18^{\circ}=\mathrm{x}=\sqrt{5}+1\) \(\Rightarrow \mathrm{x}-1=\sqrt{5}\) Squaring both sides, we get \(x^{2}-2 x+1=5\) \(\Rightarrow x^{2}-2 x-4=0\)
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