Consider the difference P=cosθ−cosϕ where θ and ϕ are acute angles close to each other.
(a) Rewrite P in a form that uses sines of half–sum and half–difference of the two angles.
(b) Explain why the rewritten form allows you to predict the sign (positive or negative) of P when θ and ϕ are very close.
(c) Without using a calculator, decide whether cos51∘−cos49∘ is positive, negative, or zero, and justify your answer.