Homework Sourse4 sin2 2x lessthanorequalto 1 0 piSolution4sin22x x pi12 or
4 sin^2 2x lessthanorequalto 1, [0, pi]![4 sin^2 2x lessthanorequalto 1, [0, pi]Solution4sin^2(2x) <=1 [0, pi] 4sin^2(2x) - 1<=0 Putting 4sin^2(2x) - 1 = 0 sin^2(2x) = 1/4 Taking square root bot](/WebImages/12/4-sin2-2x-lessthanorequalto-1-0-pisolution4sin22x-x-pi12-or-1010602-1761521641-0.webp "4 sin^2 2x lessthanorequalto 1, [0, pi]Solution4sin^2(2x) <=1 [0, pi] 4sin^2(2x) - 1<=0 Putting 4sin^2(2x) - 1 = 0 sin^2(2x) = 1/4 Taking square root bot")
Solution
4sin^2(2x) <=1 [0, pi]
4sin^2(2x) - 1<=0
Putting 4sin^2(2x) - 1 = 0
sin^2(2x) = 1/4
Taking square root both sides,
=> sin2x = 1/2 or sin2x = -1/2
When sin2x = 1/2
2x = pi/6 or pi - pi/6 = 5pi/6
=> x = pi/12 or x = 5pi/12
When sin2x = -1/2
2x = -pi/6
x = -pi/12
But x lies between 0 and pi
=> x belongs to (pi/12, 5pi/12)
