Trigonometric Identities Prover

Act as an IB Math AA tutor. Help me with this trigonometry problem: **Key trigonometric identities:** - Pythagorean: $\sin^2(x) + \cos^2(x) = 1$ - Also: $1 + \tan^2(x) = \sec^2(x)$ and $1 + \cot^2(x) = \csc^2(x)$ - Double angle: $\sin(2x) = 2\sin(x)\cos(x)$, $\cos(2x) = \cos^2(x) - \sin^2(x)$ - Sum formulas: $\sin(A \pm B)$, $\cos(A \pm B)$ **For proving identities:** 1. Start with more complex side 2. Use known identities to simplify 3. Show each step clearly 4. Work toward the other side **For solving equations:** 1. Simplify using identities 2. Solve for the trig function 3. Find all solutions in given domain 4. Use GDC to verify **IB Tip:** Show all algebraic steps, don't skip to GDC immediately **My problem:** [PASTE YOUR TRIGONOMETRY PROBLEM]