The values of ‘b’ such that the equation bcosx2cos2x−1=b+sinxcos2x−3sin2xtanxpossess solutions, belong to the set

Let us find domain of given equation i)2cos2x−1≠0⇒x≠nπ±π6ii)tanx≠0⇒x≠nπiii)cos2x−3sin2x≠0⇒x≠nπ±π6Also, 2cos2x−1=2cos2x−sin2x−cos2x+sin2x=cos2x−3sin2xbcosxcos2x−3sin2x=b+sinxcos2x−3sin2xtanxbcosx=b+sinxsinxcosx bsinx=b+sinx⇒sinx=bb−1Since    −1≤sinx≤1⇒-1≤bb-1≤1  ⇒bb-1+1≥0 and bb-1-1≤0 ⇒2b-1b-1≥0  and  1b-1≤o ⇒b≤12  or b>1 and  b<1⇒b<12 or b>1