So there is this problem
If sinα*cosα = 1/2,
and α ranges from (π ; 3π/2),
how much is sinα + cosα?
Thanks a lot!
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What I would do: $\displaystyle (sin(a)+ cos(a))^2= sin^2(a)+ 2sin(a)cos(a)+ cos^2(a)= 1+ 2sin(a)cos(a)$. Since we are given that $\displaystyle sin(a)cos9(a)= \frac{1}{2}$, $\displaystyle (sin(a)+ cos(a))^2= 1+ 1= 2$ so $\displaystyle sin(a)+ cos(a)$ is either $\displaystyle \sqrt{2}$, or $\displaystyle -\sqrt{2}$.
Between $\displaystyle \pi$ and $\displaystyle 3\pi/2$, both sin(x) and cos(x) are negative so
$\displaystyle sin(x)+ cos(x)= -\sqrt{2}$.