The equivalent Pythagorean identity is [tex]-cos^2 \theta - 1 = -sin^2 \theta[/tex]
Pythagoras theorem
According to the theorem;
[tex]x^2 + y^2 = r^2[/tex]
Given the following
x = [tex]r cos \theta[/tex]
y = [tex]r sin \theta[/tex]
Substitute into the formula
[tex](rcos \theta)^2 + (r sin \theta)^2 = r^2\\cos^2 \theta + sin^2 \theta =1[/tex]
Multiplying through by minus, the equivalent Pythagorean identity is [tex]-cos^2 \theta - 1 = -sin^2 \theta[/tex]
Learn more on Pythagoras theroem here: https://brainly.com/question/343682