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

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Answer 1 · 2018-04-27T23:27:06

$1$ $1$

$cos^2x+cos^2(π/2-x)$

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 · 2018-04-28T04:25:05

1

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