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 a, b, c are natural numbers and $\gcd(a, c) = 1$, then $a + b + c$ is equal to :

JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 8 April 2024, Shift 2, Maths Q20

Question 20 of 90 in this shift, Maths question 20 of 30, Section A.

If the value of

\frac{3\cos 36^\circ + 5\sin 18^\circ}{5\cos 36^\circ - 3\sin 18^\circ}

\frac{a\sqrt{5} - b}{c}

, where a, b, c are natural numbers and

\gcd(a, c) = 1

, then

a + b + c

is equal to :

(1) $40$
(2) $50$
(3) $52$ Official answer
(4) $54$

Official answer

Option 3

NTA final key.

Chapter: Trigonometric Functions
Topic: Trigonometric Identities
Idea tested: Values of Non-Standard Specific Angles

Same idea in other shifts

Asked 6× in all

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31 Aug 2021, Shift 1 · Q77 $\mathrm{cosec}18^\circ$ is a root of the equation :MediumSingle correct
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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.