Question

How do you verify `cos^2x + cos^2(pi/2 - x) = 1`?

Answer 1

Using the identities

• `cos(x-pi/2) = sin(x)`
• `cos(-x) = cos(x)`
• `cos^2(x)+sin^2(x) = 1`

we have:

`cos^2(x)+cos^2(pi/2-x) = cos^2(x) + cos^2(-(x-pi/2))`

`=cos^2(x)+cos^2(x-pi/2)`

`=cos^2(x)+sin^2(x)`

`=1`