Question

Rezolvati in R ecuatia cos x * ctg x - ctg x -sin x = 0

Answer 1

$cos x* \frac{cosx}{sinx} - \frac{cosx}{sinx} -sinx=0 \\ cos^{2} x-cosx- sin^{2} x=0 \\ cos2x-cosx=0 \\ 2cos^2x-cosx-1=0 \\ cosx=t \\ 2t^2-t-1=0 \\ delta=1+8=9 \\ t_{1}= \frac{4}{4} =1 \\ t_{2} =- \frac{1}{2} \\ cosx=1, x=0 grade \\ cosx=- \frac{1}{2} , x=2 \pi /3$