JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
If the value of \(\frac{3 \cos 36^{\circ}+5 \sin 18^{\circ}}{5 \cos 36^{\circ}-3 \sin 18^{\circ}}\) is \(\frac{a \sqrt{5}-b}{c}\) where \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are natural numbers and \(\operatorname{gcd}(\mathrm{a}, \mathrm{c})=1\), then \(\mathrm{a}+\mathrm{b}+\mathrm{c}\) is equal to :
- A \(50\)
- B \(40\)
- C \(52\)
- D \(54\)
Answer & Solution
Correct Answer
(C) \(52\)
Step-by-step Solution
Detailed explanation
\( \frac{\frac{3(\sqrt{5}+1)}{4}+5\left(\frac{\sqrt{5}-1}{4}\right)}{5\left(\frac{\sqrt{5}+1}{4}\right)-3\left(\frac{\sqrt{5}-1}{4}\right)}=\frac{8 \sqrt{5}-2}{2 \sqrt{5}+8} \) \( =\frac{4 \sqrt{5}-1}{\sqrt{5}+4} \times \frac{\sqrt{5}-4}{\sqrt{5}-4}\)…
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