Question

Calculati E=(sin x - cos y)^2 + (sin y - cos x)^2, stiind ca x+y = pi/6

Answer 1

$x+y= \frac{ \pi }{6} = \frac{ 180 }{6} =30$
$sin30= \frac{1}{2}$
$E= (sinx-cosy)^{2} +(siny-cosx)^{2}$
$E=sin^2x+cos^2y-2sinx*cosy+sin^2y+cos^2-2siny*cosx$
[tex]E=1+1-2(sinx*cosy+cosx*siny) [/tex]
$E=2-2sin(x+y)$
$E=2-2 \frac{1}{2} =2-1=1$