Question

2sin(p4+x)sin(p4-x)+sin^2x=0

Answer 1

Используем формулу:
$sin^2a - sin^2b = sin(a+b)sin(a-b)\ \2sin(frac{pi}{4}+x)sin(frac{pi}{4}-x)+sin^2x=0\2sin^2frac{pi}{4}-2sin^2x+sin^2x=0\2*(frac{sqrt2}{2})^2-sin^2x=0\1-sin^2x=0\sinx=pm1\\1)sinx=1\x=frac{pi}{2}+2pi n, ; nin Z;\\2)sinx=-1\x=-frac{pi}{2}+2pi k, ; kin Z.$