$f(x) = \sin x + 2\cos x$$ \Rightarrow f(\frac{\pi }{3}) = \sin \frac{\pi }{3} + 2\cos \frac{\pi }{3} = \frac{{\sqrt 3 }}{2} + 2 \times \frac{1}{2} = \frac{{\sqrt 3 }}{2} + 1$$f(\frac{\pi }{4}) = \sin \frac{\pi }{4} + 2\cos \frac{\pi }{4} = \frac{{\sqrt 2 }}{2} + \frac{{2\sqrt 2 }}{2} = \frac{{\sqrt 2 }}{2} + \sqrt 2 $$ \Rightarrow f(\frac{\pi }{3}) + f(\frac{\pi }{4}) - 1 = \frac{{\sqrt 3 }}{2} + 1 + \frac{{\sqrt 2 }}{2} + \sqrt 2  - 1 = \frac{{\sqrt 3  + 3\sqrt 2 }}{2}$