Final answer:
The expression csc x cot x (1 - cos^2 x) simplifies to cos x * sin x, which is the product of the sine and cosine functions for angle x.
Step-by-step explanation:
The expression given is csc x cot x (1 - cos^2 x). Using trigonometric identities, we can simplify this expression. It is known that csc x is the reciprocal of sin x, so csc x = 1/sin x, and cot x is the reciprocal of tan x, or cos x/sin x.
Also, because sin^2 x + cos^2 x = 1, the term (1 - cos^2 x) can be replaced with sin^2 x. Substituting these into our given expression, we have:
- csc x * cot x * sin^2 x = (1/sin x) * (cos x/sin x) * sin^2 x.
This simplifies to:
Thus the original expression simplifies to cos x * sin x, which is the product of the sine and cosine functions for angle x.