141k views
4 votes
Show that the equation is not an identity. sec²(x) + csc²(x) =1

1 Answer

5 votes

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.

User Walta
by
8.1k points

Related questions

asked Apr 13, 2024 220k views
Hamid Asghari asked Apr 13, 2024
by Hamid Asghari
7.4k points
1 answer
5 votes
220k views
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.