Question

а) 2cos(pi/4+x)=корень из 2
б) -2sin(2x+pi/3)-1=0

Answer 1

а)
2 cos (π/4 +x) = √2
cos (π/4 +x) = √2/2

π/4 + x = π/4 + 2πm, m ∈ Z - 1 корень
π/4 + x = - π/4 + 2πn, n ∈ Z - 2 корень

π/4 + x - π/4 = 2πm, m ∈ Z 
π/4 + x + π/4 = 2πn, n ∈ Z 

x = 2πm, m ∈ Z
x = 2πn - π/2, n ∈ Z

Ответ: -π/2 + 2πn, n∈Z; 2πm, m ∈ Z

Answer 2

$a); 2cos(frac{pi}{4}+x)=sqrt 2\cos(frac{pi}{4}+x)=frac{sqrt2}{2}\frac{pi}{4}+x=pm frac{pi}{4}+2pi n\\x_1=frac{pi}{4}-frac{pi}{4}+2pi n\x_1=2pi n, ; nin Z;\\x_2=-frac{pi}{4}-frac{pi}{4}+2pi n\x_2=-frac{pi}{2}+2pi n, ; nin Z;\\ b);-2sin(2x+frac{pi}{3})-1=0\sin(2x+frac{pi}{3})=-frac{1}{2}\2x+frac{pi}{3}=(-1)^{n+1}frac{pi}{3}+pi n\2x=(-1)^{n+1}frac{pi}{3}-frac{pi}{3}+pi n\x=frac{1}{2}*(-1)^{n+1}frac{pi}{3}-frac{pi}{6}+frac{pi n}{2},;nin Z.$