Final answer:
To show that the equation sec²(x) + csc²(x) = 1 is not an identity, we can simplify both sides of the equation and check if they are equal for all values of x.
Step-by-step explanation:
To show that the equation sec²(x) + csc²(x) = 1 is not an identity, we can simplify both sides of the equation and check if they are equal for all values of x. Starting with the left side of the equation:
sec²(x) + csc²(x).
Using the identities tan²(x) + 1 = sec²(x) and 1 + cot²(x) = csc²(x), we can rewrite the equation as:
tan²(x) + 1 + 1 + cot²(x).
Simplifying further, we have:
tan²(x) + cot²(x) + 2.
Since tan²(x) + cot²(x) is always greater than or equal to 2, the right side of the equation will always be greater than the left side. Therefore, sec²(x) + csc²(x) is not equal to 1 for all values of x, and it is not an identity.