Question

How do you simplify: cos^2x+cos^2(π/2-x) ?

Answer 1

`1`

Explanation:

`cos^2x+cos^2(π/2-x)`

Can be rewritten as:
`cos^2x+cos(π/2-x)*cos(π/2-x)`

Apply cosine difference identity:
`cos^2x+(cos(pi/2)*cosx+sin(pi/2)sinx)(cos(pi/2)*cosx+sin(pi/2)sinx)`

Simplify:
`cos^2x+(0*cosx+1*sinx)(0*cosx+1*sinx)`

`cos^2x+(sinx)(sinx)`

`cos^2x+sin^2x`

Apply the Pythagorean identity:
`1`

Answer 2

1

Explanation:

Trig identity:
`cos (pi/2 - x) = sin x`
Therefor,
`cos^2 x + cos^2 (pi/2 - x) = cos^2 x + sin^2 x = 1`