Tip 1: Always check which principal value branch the answer must lie in — many errors come from forgetting the range. Tip 2: For tan^(-1) addition, immediately check if xy < 1 or xy > 1 before applying the formula. Tip 3: When a problem asks for a numerical value, expect clean answers like pi/4, pi/3, pi/6, or pi. Tip 4: For telescoping sums, try writing the general term as tan^(-1)(A) - tan^(-1)(B) by partial fractions on the argument. Tip 5: When converting between inverse trig types, draw the right triangle — it prevents sign and domain errors. Tip 6: For equations, try substitution (let theta = sin^(-1)(x)) to convert to a standard trig equation, solve for theta, then recover x = sin(theta).