Express 2cosx+2sinx\sqrt{2} \cos x + \sqrt{2} \sin x2cosx+2sinx in the form Rcos(x−a)R \cos(x - a)Rcos(x−a) where R>0 R > 0\,R>0 and 0≤a≤π2\displaystyle 0 \leq a \leq \frac{\pi}{2}0≤a≤2π
Write down the range of the function
f(x)=3+2cosx+2sinx0≤x<2π f(x) = 3 + \sqrt{2} \cos x + \sqrt{2} \sin x \quad 0 \leq x < 2\pi f(x)=3+2cosx+2sinx0≤x<2π348 exam-style questions on Edexcel A Level Maths Trigonometry and Modelling, covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.