Equation `cos 2x+7=a(2-sin x)` can have a real solution for

The equation |x+1||x-1|=a^(2) - 2a - 3 can have real solutions for x, if a belongs to

The equation |x+1||x-1|=a^(2) - 2a - 3 can have real solutions for x, if a belongs to

The equation abs(x+1) abs(x-1)=a^2-2a-3 can have real solutions for x if 'a' belongs to

Prove that the equation cos 2x + a sin x = 2a - 7 possesses a solution if 2 le a le 6 .

Show that the equation sin x(sin x+cos x)=a has real solution if and only if a is a real number lying between (1)/(2)(1-sqrt(2)) and (1)/(2)(1+sqrt(2))

The set of values of 'a' for which the equation "sin" x ("sin"x +"cos" x) = a has real solutions, is