If ` 2 cos x lt sqrt(3) and x in [-pi, pi]` , then find the solution set for x .

If cos x- sin x ge 1 and 0 le x le 2pi , then find the solution set for x .

If cos x- sin x ge 1 and 0 le x le 2pi , then find the solution set for x .

If cos x- sin x ge 1 and 0 le x le 2pi , then find the solution set for x .

If cos x- sin x ge 1 and 0 le x le 2pi , then find the solution set for x .

Assertion (A) : cos x = (-1)/(2) and 0 lt x lt 2pi, "then the solutions are x" = (2pi)/(3), (4pi)/(3) . Reason (R ) : cos is negative in the first and fourth quadrant only

if cos x= (-sqrt(15))/(4) " and " (pi)/(2) lt x lt pi find the value of sin x .

if cos x= (-sqrt(15))/(4) " and " (pi)/(2) lt x lt pi find the value of sin x .

if cos x= (-sqrt(15))/(4) " and " (pi)/(2) lt x lt pi find the value of sin x .

Let f(x) = {{:(-2 sin x,"for",-pi le x le - (pi)/(2)),(a sin x + b,"for",-(pi)/(2) lt x lt (pi)/(2)),(cos x,"for",(pi)/(2) le x le pi):} . If f is continuous on [-pi, pi) , then find the values of a and b.

Let f(x) = {{:(-2 sin x,"for",-pi le x le - (pi)/(2)),(a sin x + b,"for",-(pi)/(2) lt x lt (pi)/(2)),(cos x,"for",(pi)/(2) le x le pi):} . If f is continuous on [-pi, pi) , then find the values of a and b .