JEE Mains · Maths · STD 11 - Trigonometrical equations
\(\alpha=\sin 36^{\circ}\) is a root of which of the following equation
- A \(10 x^{4}-10 x^{2}-5=0\)
- B \(16 x^{4}+20 x^{2}-5=0\)
- C \(16 x^{4}-20 x^{2}+5=0\)
- D \(16 x^{4}-10 x^{2}+5=0\)
Answer & Solution
Correct Answer
(C) \(16 x^{4}-20 x^{2}+5=0\)
Step-by-step Solution
Detailed explanation
\(\cos 72^{\circ}=\frac{\sqrt{5}-1}{4}\) \(\Rightarrow 1-2 \sin ^{2} 36^{\circ}=\frac{\sqrt{5}-1}{4}\) \(\Rightarrow 4-8 \alpha^{2}=\sqrt{5}-1\)4 \(\Rightarrow 5-8 \alpha^{2}=\sqrt{5}\) \(\Rightarrow\left(5-8 \alpha^{2}\right)^{2}=5\)…
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