The five moves
- Turn everything into sin and cos.
- Spot Pythagoras in disguise (1 − cos²θ, 1 − sin²θ, sec²θ − 1…)
- Combine fractions over one denominator.
- Multiply by the conjugate (1 ± sin θ, 1 ± cos θ)
- Factorise and cancel — legally.
Prove that
The working — one legal line at a time
∴ LHS = RHS ∎
Which line comes next?