Question

Срочно нужна помощь!

Answer 1

$displaystyle 16^{cos^2x}+16^{sin^2x}=10\\16^{cos^2x}+16^{1-cos^2x}=10\\16^{cos^2x}+ frac{16}{16^{cos^2x}}=10\\16^{cos^2x}=t\\t+ frac{16}{t}=10\\ frac{t^2+16-10t}{t}=0\\t^2-10t+16=0\\D=100-64=36\\t_{1.2}= frac{10pm 6}{2}\\t_1=8; t_2=2$

$displaystyle 16^{cos^2x}=8\\(2^4)^{cos^2x}=2^3\\4cos^2x=3\cos^2x= frac{3}{4}\\cosx=pm frac{ sqrt{3}}{2}\\x_{1.2}=pm frac{ pi }{6}+2 pi n; nin Z\\x_{3.4}=pm frac{5 pi }{6}+2 pi n; nin Z$


$displaystyle 16^{cos^2x}=2\\2^{4cos^2x}=2\\4cos^2x=1\\cos^2x= frac{1}{4}\\cosx= pm frac{1}{2}\\x_{5.6}=pm frac{ pi }{3}+2 pi n; nin Z\\x_{7.8}=pm frac{2 pi }{3}+2 pi n; nin Z$