# is \$sin(a)=sqrt{1-cos^2(a)}\$ derived from \$sin^2(a)+cos^2(a)=1\$

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