Question

Why don’t we ever have cause to use the trigonometric substitution $x=\cos u$?

Short answer

Ans: In terms of the Pythagorean identity, sine and cosine behave the same way. That's why we can always use $x=\sin u$ instead of $x=\cos u$.

Step-by-step solution

Step 1. Given information.

given,

$x=\cos u$

Step 2.  Solution:-

In terms of the Pythagorean identity, sine and cosine behave the same way. That's why we can always use $x=\sin u$ instead of $x=\cos u$.