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JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

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Application +4 | -1
If the value of 3cos⁡36∘+5sin⁡18∘5cos⁡36∘−3sin⁡18∘\frac{3 \cos 36^{\circ}+5 \sin 18^{\circ}}{5 \cos 36^{\circ}-3 \sin 18^{\circ}} is a5−bc,\frac{\mathrm{a} \sqrt{5}-\mathrm{b}}{\mathrm{c}}, where a,b,c\mathrm{a}, \mathrm{b}, \mathrm{c} are natural numbers and gcd⁡(a,c)=1,\operatorname{gcd}(\mathrm{a}, \mathrm{c})=1, then a+b+c\mathrm{a}+\mathrm{b}+\mathrm{c} is equal to:
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Correct option: C
52
Option C (52) is correct because after simplifying the given expression using trigonometric values and rationalizing the denominator, the values of a, b, and c can be determined, and their sum is 52.

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