Question

(sin x+cos x)la a 2a minus sin 2x egal cu 1,pentru orice nr real x

Answer 1

"(sin x+cos x)la a 2a minus sin 2x egal cu 1"

(sinx + cosx)^2 - sin2x = 1

$\it (sinx + cosx)^2 - sin2x = 1 \Leftrightarrow sin^2x+2sinxcosx+cos^2x-sin2x=1\Leftrightarrow\\ \\ \Leftrightarrow sin^2x+cos^2x+sin2x-sin2x=1 \Leftrightarrow 1=1\ (Adev\breve{a}rat)$