Question

докажите тождество sinx-cosx=-√2cos(π/4+х)

Answer 1

$sinx-cosx = -sqrt{2}(cos frac{ pi }{4}+x) \ -sqrt{2}cos( frac{ pi }{4}+x) =$
$sqrt{2}(cos frac{ pi }{4}*cosx-sin frac{ pi }{4}*sinx) = - sqrt{2} ( frac{ sqrt{2} }{2}*cosx- frac{ sqrt{2} }{2}sinx) =$ $-sqrt{2}* frac{ sqrt{2} }{2}(cosx-sinx) = -frac{2}{2}(cosx - sinx)=-(cosx - sin x)=$ $sinx-cosx$