Solving Trigonometric Equations Using Sum/Difference Identities
Consider the trigonometric equation: \(\sin(x+\pi/3) = \sqrt{2}/2\). Solve for \(x\) in the interval \([0, 2\pi]\). This question is divided into three parts:
Part a
Apply the sine angle sum identity to express \(\sin(x+\pi/3)\) in terms of \(\sin x\) and \(\cos x\).