[PreCalculus] Proving Identities

[Snowglober]

Homework Statement

Prove that this is an identity.

1 + cos² x / sin² x = 2csc² - 1

Homework Equations

cos²x + sin²x = 1 (manipulative equation)
tan²x = sec² - 1
cot²x = csc²x - 1
etc..

The Attempt at a Solution

I attempted this equation more than 10+ times. Each time, I find a way but I get half way there and it doesn't work out.

 

[rl.bhat]

Hi Snowglober, welcome to PF
The problem should be
(1 + cos^2x)/sin^2x = 2csc^2x - 1
Now LHS can be written as
1/sin^2x + cos^2x/sin^2
= csc^2x + cot^2x
Now use the identities to get the result.

 

[fatima_a]

this website really helped me understand identities. do read through the whole thing

http://www.intmath.com/Analytic-trigonometry/1_Trigonometric-identities.php