JEE Mains · Maths · STD 11 - Trigonometrical equations
Let in a right angled triangle, the smallest angle be \(\theta\). If a triangle formed by taking the reciprocal of its sides is also a right angled triangle, then \(\sin \theta\) is equal to:
- A \(\frac{\sqrt{5}+1}{4}\)
- B \(\frac{\sqrt{5}-1}{2}\)
- C \(\frac{\sqrt{2}-1}{2}\)
- D \(\frac{\sqrt{5}-1}{4}\)
Answer & Solution
Correct Answer
(B) \(\frac{\sqrt{5}-1}{2}\)
Step-by-step Solution
Detailed explanation
\(\,<\,A=\theta\) \(\,<\,B=90^{\circ}-\theta\) \(c^{2}=a^{2}+b^{2}\) \(\frac{1}{a} \rightarrow\) largest side \(\therefore \frac{1}{a^{2}}=\frac{1}{b^{2}}+\frac{1}{c^{2}}\) \(\frac{\mathrm{b}^{2} \mathrm{c}^{2}}{\mathrm{a}^{2}}=\mathrm{b}^{2}+\mathrm{c}^{2}\) Use…
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