Quick questions on Trigonometric identities and equations: double angle, the R form and solving - OCR A-Level Maths A

Solve a trigonometric equation by reducing it to a single function, finding the principal value, then using the symmetry of the graph to find every solution in the interval. Beware of intervals on a transformed argument such as $2x$ or $x + 30^\circ$: widen the interval for the argument before solving, then convert back.

To prove an identity, work on the more complicated side and reduce it to the other using the core identities. Never move terms across the $\equiv$ sign as if solving an equation.

Forgetting to widen the interval for a transformed argument. For $\sin 2x$ over $0$ to $360^\circ$, the argument $2x$ runs to $720^\circ$, so there are more solutions than you might expect.

Express $\sin\theta + \sqrt{3}\cos\theta$ in the form $R\sin(\theta + \alpha)$. [3 marks]

Solve $\tan x = 2\sin x$ for $0^\circ \le x \le 360^\circ$. [3 marks]