I have a problem of `$cos(a)=t`

for $270<=a<=360$

$a)cos(90+a)$

for obvious , my answer is the answer is

$cos(90)cos(a)-sin(90)sin(a)$ and left me with

$=-sin(a)$

But what is the proof $sin(a)=sqrt{(1-cos^2(a)}$

$sin^2(a)+cos^2(a)=1$

$sin^2(a)=1-cos^2(a)$

$sin(a)=sqrt{1-cos^2(a)}$

my friend said that , this is false

What is the real solution or proof to the $sin(a)=sqrt{(1-cos^2(a)}$?