Question

dacă tg x=1,atunci sin x+cos x = ??

Answer 1

$\text{tg }x = 1 \Rightarrow \dfrac{\sin x}{\cos x} = 1 \Rightarrow \sin x = \cos x \Rightarrow \sin x - \cos x = 0\\ \\ \sin x - \cos x = 0\Big|^2 \\ \sin^2 x+ \cos^2 x-2\sin x\cos x = 0\\ 1-\sin 2x = 0 \\ \Rightarrow \sin 2x = 1\\ \\ E = \sin x+\cos x\\ E^2 = \sin^2 x +\cos^2 x +2\sin x\cos x \\ E^2 = 1+\sin 2x\\ E^2 = 1+1 \\ E^2 = 2 \\ \Rightarrow E = \pm \sqrt 2 \\ \\ \Rightarrow \sin x+\cos x = \pm \sqrt 2$