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1 solution
This is a non rigorous solution and I do not recommend it using it for similar/related questions.
Note that RHL, 1 3 + 2 cos ( x ) can attain values 1 1 , 1 3 , 1 5 . All odds.
The LHL is the sum of two even terms, each multiplied by an integer. Since, an even number multiplied by any integer gives an even integral value, it can never return odd terms.
Hence, we infer zero solutions.