Chapter 13.6, Problem 14OE

To determine

To Find: The reason why the given equation is incorrect.

Answer to Problem 14OE

The $x$ can be any angle thus, it is incorrect to divide both the sides by $\cos x$ .

Explanation of Solution

Given:

The given expression is $\frac{\cos x}{{\sin }^{2}x}=\cos x{\csc }^{2}x$ .

Calculation:

Consider the given expression is,

  $\frac{\cos x}{{\sin }^{2}x}=\cos x{\csc }^{2}x$

Divide bot the sides by $\cos x$ as,

  $\frac{1}{{\sin }^{2}x}={\csc }^{2}x$

The above equation may or may not be equal as both the sides are squared and the values may be unique on both the sides.

Consider that in the equation ${\sin }^{2}x$ , $x$ can be any angle thus, it is incorrect to divide both the sides by $\cos x$ .