jee-main 2024 Q65

jee-main · India · session2_08apr_shift2 Reciprocal Trig & 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 $a , b , c$ are natural numbers and $\operatorname { gcd } ( a , c ) = 1$, then $a + b + c$ is equal to : (1) 40 (2) 52 (3) 50 (4) 54
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 $\operatorname { gcd } ( a , c ) = 1$, then $a + b + c$ is equal to :
(1) 40
(2) 52
(3) 50
(4) 54