Final answer:
To prove that cot a - cos a = cot a cos a, we can start by expressing cot a as cos a / sin a and simplify accordingly. The final equation is 1 - sin a = cos a, which is true according to the Pythagorean trigonometric identity.
Step-by-step explanation:
To prove that cot a - cos a = cot a cos a, we can start by expressing cot a as cos a / sin a. So the equation becomes cos a / sin a - cos a = cos a * cos a / sin a.
Next, we can find a common denominator for the left side of the equation, which is sin a. So the equation becomes cos a - cos a * sin a / sin a = cos a * cos a / sin a.
Simplifying further, we get cos a - cos a * sin a = cos a * cos a.
Factor out cos a from the left side of the equation, and we have cos a * (1 - sin a) = cos a * cos a.
Finally, divide both sides of the equation by cos a, and we get 1 - sin a = cos a. And this equation is true since it represents the identity of the Pythagorean trigonometric identity.