đặt \(\sin a=\dfrac{x}{y};\cos a=\dfrac{z}{y}\)
Ta có : \(\sin a+\cos a=\sqrt{2}\)
\(\dfrac{x}{y}+\dfrac{z}{y}=\sqrt{2}\Rightarrow\dfrac{x+z}{y}=\sqrt{2}\)
\(\Rightarrow\dfrac{\left(x+z\right)^2}{y^2}=2\)
Mà ta có: x2+z2=y2(pitago)
\(\Rightarrow\dfrac{x^2+z^2+2xz}{x^2+z^2}=2\Rightarrow1+\dfrac{2xz}{x^2+z^2}=2\)
\(\Rightarrow\dfrac{2xz}{x^2+z^2}=1\Rightarrow2xz=x^2+z^2\Rightarrow x=z\)
=>\(a=45^o\)
=>\(\sin a=\sin45=\dfrac{\sqrt{2}}{2}\)
\(\cos a=\cos45=\dfrac{\sqrt{2}}{2}\)
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