Porisma

A hint to get started

Track the order of an approximation through division

If θ\theta is sufficiently small for θ3\theta^3 and higher powers of θ\theta to be neglected, find approximations for

(a) sin⁡θcos⁡2θ\dfrac{\sin\theta}{\cos2\theta},

(b) θtan⁡θ1−cos⁡θ\dfrac{\theta\tan\theta}{1-\cos\theta}.

CJC · Lecture · Example 10

Rewrite with exact identities first, then retain enough terms to survive any multiplication, cancellation or division.

Read the worked solution