Final answer:
The expression 1 - 4sin² a can be re-written as -2 * cos 2a by using the double angle identity for cosine.
Step-by-step explanation:
The question asks us to express the trigonometric expression 1 - 4sin² a as a product. This can be done by using the trigonometric identity for the cosine of a double angle, which states that cos 2a = 1 - 2sin² a. By comparing the given expression with the identity, we can deduce that the given expression is twice the negative of the double angle identity for cosine, which can be written as:
(-2)(2sin² a - ½)
Therefore, the expression 1 - 4sin² a can be expressed as the product:
-2 * cos 2a.