Answer:
[tex]Cot^2\theta-Csc^2\theta=-1[/tex]
Step-by-step explanation:
The only Pythagorean identities are:
[tex]1. \ Sin^2\theta+Cos^2\theta=1[/tex]
[tex]2. \ 1+Tan^2\theta=Sec^2\theta[/tex]
[tex]3. \ 1+Cot^2\theta=Csc^2\theta[/tex]
[tex]4. \ Sin^2\theta=1-Cos^2\theta\\ \ \ Cos^2\theta=1-Sin^2\theta[/tex]
Therefore,[tex]Cot^2\theta-Csc^2\theta=-1[/tex] is correct as it's one of the pythagorean identities.
The true equation of the Pythagorean identity is [tex]\cot^2(\theta) - \csc^2(\theta) = -1[/tex]
A Pythagorean identity is represented as:
[tex]\sin^2(\theta) +\cos^2(\theta) = 1[/tex]
Divide through by sin^2(theta)
[tex]\frac{\sin^2(\theta)}{\sin^2(\theta)} +\frac{\cos^2(\theta)}{\sin^2(\theta)} = \frac{1}{\sin^2(\theta)}[/tex]
Evaluate the quotients
[tex]1 + \cot^2(\theta) = \csc^2(\theta)[/tex]
Rewrite as:
[tex]\cot^2(\theta) - \csc^2(\theta) = -1[/tex]
Hence, the true equation of the Pythagorean identity is [tex]\cot^2(\theta) - \csc^2(\theta) = -1[/tex]
Read more about Pythagorean identity at:
https://brainly.com/question/95257
