Question

Identify the Pythagorean identity from the following.sin2 x - cos2 x = 1sin2 x + cos2 x = 1sin2 x - cos2 x = 0sin2 x + cos2 x = 0

Answer 1

In the unit circle

The radius of the circle = 1

At any point (x, y) on the circle

x-coordinate = cos(x)

y-coordinate = sin(x)

Then to find the radius of the circle we will use the Pythagorean Theorem

$\begin{gathered} x^2+y^2=r^2 \\ \\ x^2+y^2=1 \end{gathered}$

Substitute x by cos(x) and y by sin(x)

$\begin{gathered} cos^2x+sin^2x=1 \\ \\ sin^2x+cos^2x=1 \end{gathered}$

The correct identity is the 2nd choice

$sin^2x+cos^2x=1$