Mathematics - Trigonometry - Advanced - Trigonometric identities - Simplify and Prove
10 problems: (1) Simplify expressions using identities: 'sin²x + cos²x + tan²x' = 1+tan²x = sec²x. (2) Prove identities: show left side = right side. (3) Given one trig value and the quadrant, find all others: 'sinθ=3/5, θ in Q1, find cosθ, tanθ.' Include multi-step simplifications and proofs.