Question

1)cos^2x=1/2+sin^2x 2)4sinxcosx cos 2x=1 3)sinx*cos(x+pi/3)+cosx*sin(x+pi/3)=0

Answer 1

1/   $cos^2x-sin^2x=frac{1}{2}\ cos2x=frac{1}{2}\ 2x=+-frac{pi}{3}+2pi*k\ x=+-frac{pi}{6}+pi*k$

2/   $sin2x=2sinx*cosx\ sin4x=2sin2x*cos2x=4sinx*cosx*cos2x\ 4sinx*cosx*cos2x=1\ sin4x=1\ 4x=frac{pi}{2}+2pi*n\ x=frac{pi}{8}+frac{pi*n}{2}$

3/   $sin(a+b)=sina*cosb+cosa*sinb\ sinx*cos(x+frac{pi}{3})+cosx*sin(x+frac{pi}{3})=0\ sin(x+x+frac{pi}{3})=0\ 2x+frac{pi}{3}=pi*k\ x=frac{pi*k}{2}-frac{pi}{6}$