If p≤(cos2x+6sinx-1)≤q, then (p,q)=

a.(-8,4)

b.(4,8)

c.(-4,8)

d.none of these

Hi Menka,

Form a Quadratic in sinx, by the substitutung for cos2x in terms of sin^2 x.

So you have p≤6sinx-sin^2 x≤q.

Minimum value obtained by substituting sinx=-1 and max value obtained by sinx=1

So p=-8 and q=4.

Which is option (A) but with closed brackets.

Hope that helps.

Best Regards,

Ashwin (IIT Madras).