Răspuns:
[tex]e= \frac{\frac{1}{2}*[sin(x+2y)+sinx]-\frac{1}{2}*[sin(x+2y)+sin(-x)]}{\frac{1}{2}*[cos(-x)+cos(x+2y)]+\frac{1}{2}*[cosx-cos(x+2y)]} \\\\e= \frac{sin(x+2y)+sinx-sin(x+2y)-(-sinx)}{cosx+cos(x+2y)+cosx-cos(x+2y)} \\e= \frac{2sinx}{2cosx} \\e= \frac{sinx}{cosx} \\e=tgx[/tex]
Explicație pas cu pas:
se folosesc formulele:
[tex]sin a * cosb = \frac{1}{2} [sin(a+b)+sin(a-b)]\\cos a * cosb = \frac{1}{2} [cos(a-b)+cos(a+b)]\\sin a * sinb = \frac{1}{2} [cos(a-b)-cos(a+b)][/tex]
