$f'(x) = a \cos x + b \sin x ;\; f'(0)=4;\; f(0)=3;\; f \bigg(\large\frac{\pi}{2}\bigg)$$=5$. Find the value of $\;f(x)\;$?

Question

$(a)\;4 \tan x + 2 \cot x +1\qquad(b)\;4 \sin x + 2 \cos x +1\qquad(c)\;4 \cos x + 2 \sin x +1\qquad (d)\;\cos x + \sin x$