The statement " is true for all real numbers ".

The trigonometric equation is .

Consider left hand side identity : .

Apply reciprocal identity : .

Apply quotient identity : .

Apply reciprocal identity : .

= Right hand side identity.

But, these expressions are not defined for all real numbers.

For example, , and are undefined.

The domain does not include the values of where is undefined, such as .

Thus, the statement is false.

False.