I need some help solving these trig equations. Thanks for help on any

tan^2(x) + sec(x)= 1

Tan(x) cos(x)=1/2

Sqr root(2sin^3(x) = sin^2(x)

Sqr root(2cos^2(x) = cos^2(x)

On the two problems with the sqr root. On the sheet it only has the line over the 2 so i dont know if its across the entire thing