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$2) (64^{cosx})^{sinx}=4^{frac{3cosx}{2}}; x E [-pi;frac{pi}{2}] (4^3)^{cosx*sinx}=4^{frac{3cosx}{2}} 4^{3cosx*sinx}=4^{frac{3cosx}{2}} 3cosx*sinx=frac{3cosx}{2} 6cosx*sinx=3cosx 6cosx*sinx-3cosx=0 3cosx(2sinx-1)=0 |3cosx=0 |2sinx-1=0 |cosx=0 |sinx=frac{1}{2} |x=frac{pi}{2}+pi k |x=frac{pi}{3}+2pi k |x=frac{2pi}{3}+2pi k$
$x E [-pi;frac{pi}{2}] 1) -pi leq frac{pi}{2}+pi k leq frac{pi}{2} -frac{3pi}{2} leq pi k leq 0 -1frac{1}{2} leq k leq 0 = textgreater k=0; k=-1 k=0 = textgreater x = frac{pi}{2} k=1 = textgreater x = frac{pi}{2}-pi=-frac{pi}{2} 2) -pi leq frac{pi}{3}+2pi k leq frac{pi}{2} -frac{4pi}{3} leq 2pi k leq frac{pi}{6} -frac{2}{3} leq k leq frac{1}{12} = textgreater k = 0 k = 0 = textgreater x=frac{pi}{3}$
$3) -pi leq frac{2pi}{3}+2pi k leq frac{pi}{2} -frac{5pi}{3} leq 2pi k leq -frac{pi}{6} -frac{5}{6} leq k leq -frac{1}{12}$
$3) 2cos^2x = sin(frac{3pi}{2}+x); x E [-frac{7pi}{2};-2pi] 2cos^2x=-cosx 2cos^2x+cosx=0 cosx(2cosx+1)=0 |cosx=0 |2cosx+1=0 |cosx=0 |cosx=-frac{1}{2} |x=frac{pi}{2}+pi k |x=+-frac{2pi}{3}+2pi k$
$x E [-frac{7pi}{2};-2pi] 1) -frac{7pi}{2} leq frac{pi}{2}+pi k leq -2pi -4pi leq pi k leq -frac{5pi}{2} -4 leq k leq -2frac{1}{2} = textgreater k=-4; k=-3 k=-4 = textgreater x=frac{pi}{2}-4pi=-frac{7pi}{2} k=-3 = textgreater x=frac{pi}{2}-3pi=-frac{5pi}{2}$
$2) -frac{7pi}{2} leq frac{2pi}{3}+2pi k leq -2pi -frac{25pi}{6} leq 2pi k leq -frac{8pi}{3} -frac{25}{12}leq k leq -frac{4}{3} -2frac{1}{12} leq k leq -1frac{1}{3} = textgreater k = -2 k=-2 = textgreater x=frac{2pi}{3}-4pi =-frac{10pi}{3}$
$3) -frac{7pi}{2}leq -frac{2pi}{3}+2pi k leq -2pi -frac{17pi}{6}leq 2pi k leq -frac{4pi}{3} -frac{17}{12}leq k leq -frac{2}{3} -1frac{5}{12}leq k leq -frac{2}{3} = textgreater k=-1 k=-1 = textgreater x=-frac{2pi}{3}-2pi=-frac{8pi}{3}$