Question

Punctul c). Sa se arate ca.

Answer 1

[tex]\frac{cos^3x-cos3x}{cosx}+\frac{sin^3x+sin3x}{sinx}=3\\ \frac{cos^3x-4\cdot cos^3x+3cosx}{cosx}+\frac{sin^3x+3\cdot sinx-4\cdot sin^3x}{sinx}=3\\ \frac{3cosx-3cos^3x}{cosx}+\frac{3sinx-3sin^3x}{sinx}=3\\ \frac{3cosx(1-cos^2x)}{cosx}+\frac{3sinx(1-sin^2x)}{sinx}=3\\ 3(1-cos^2x)+3(1-sin^2x)=3\\ 3\cdot sin^2x+3\cdot cos^2x=3\\ 3(sin^2x+cos^2x)=3\\ 3=3(A)[/tex]