Correct option is (4) 2
\(y=\frac{2 \cos \theta+2 \cos ^{2} \theta-1}{4 \cos ^{3} \theta-3 \cos \theta+8 \cos ^{2} \theta-4+5 \cos \theta+2}\)
\(y=\frac{\left(2 \cos ^{2} \theta+2 \cos \theta-1\right)}{\left(2 \cos ^{2} \theta+2 \cos \theta-1\right)(2 \cos \theta+2)}\)
\(y=\frac{1}{2}\left(\frac{1}{1+\cos \theta}\right)\)
\(\Rightarrow \theta=\frac{\pi}{2}, y=\frac{1}{2}\)
\(y^{\prime}=\frac{1}{2}\left(\frac{-1}{(1+\cos \theta)^{2}} \times(-\sin \theta)\right)\)
\(\Rightarrow \theta=\frac{\pi}{2} , y=\frac{1}{2}\)
\(y^{\prime \prime}=\frac{1}{2}\left[\frac{\cos \theta(1+\cos \theta)^{2}-\sin \theta(2)(1+\cos \theta)(-\sin \theta)}{(1+\cos \theta)^{4}}\right]\)
\(\Rightarrow \theta=\frac{\pi}{2}, y = 1\)
\(\Rightarrow y''+y'+y = 1 + \frac12+\frac12 = 4\)