Strategy 1: For simplification, try converting everything to sin and cos first. Strategy 2: For proving identities, work on the more complex side and simplify toward the simpler side. Strategy 3: For equations, reduce to a single trig function using identities, then solve. Strategy 4: For max/min problems, use the auxiliary angle method or AM-GM inequality on trig terms. Strategy 5: For sum-type problems, use sum-to-product to factor, or multiply by a convenient factor (like 2*sin(theta) for cosine products). Strategy 6: For conditional problems with A + B + C = pi, substitute C = pi - A - B early. Strategy 7: For counting solutions in an interval, find the general solution first, then enumerate. Common JEE trap: forgetting to check validity of solutions when operations like squaring or dividing by trig expressions were performed. Always verify in the original equation.