Question

Help :sa se demonstreze ca expresia (sin x +cos ×) "la patrat" - (minus) 2sinx cox x este constanta pentru orice nr. real x​

Answer 1

$\textbf{Formule de calcul prescurtat:}\\ \diamond \,(a+b)^2 = a^2+2ab+b^2 \\\diamond\, \sin^2x+\cos^2x = 1\\ \\ \textbf{Demonstratie}:\\(\sin x+\cos x)^2 - 2\sin x\cos x = \\ =\sin^2x+2\sin x\cos x+\cos^2 x-2\sin x\cos x\\ = \sin^2 x+\cos^2 x+2\sin x\cos x-2\sin x\cos x \\ = 1+0\\= 1,\quad \forall x\in \mathbb{R}$