If the value of 5 c o s 3 6 ∘ − 3 s i n 1 8 ∘ 3 c o s 3 6 ∘ + 5 s i n 1 8 ∘ is c a 5 − b , where a , b , c are natural numbers and gcd ( a , c ) = 1 , then a + b + c is equal to :

Question

If the value of 5 c o s 3 6 ∘ − 3 s i n 1 8 ∘ 3 c o s 3 6 ∘ + 5 s i n 1 8 ∘ ​ is c a 5 ​ − b ​ , where a , b , c are natural numbers and gcd ( a , c ) = 1 , then a + b + c is equal to :

TestHub · Accepted Answer

​ 5 ( 4 5 ​ + 1 ​ ) − 3 ( 4 5 ​ − 1 ​ ) 4 3 ( 5 ​ + 1 ) ​ + 5 ( 4 5 ​ − 1 ​ ) ​ = 2 5 ​ + 8 8 5 ​ − 2 ​ = 5 ​ + 4 4 5 ​ − 1 ​ × 5 ​ − 4 5 ​ − 4 ​ ​ ​ = − 11 20 − 16 5 ​ − 5 ​ + 4 ​ = 11 17 5 ​ − 24 ​ ⇒ a = 17 , b = 27 , c = 11 a + b + c = 52 ​

Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

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