Let cos2⁡θ+b and sin2⁡θ+b are roots of the equation x2+4x+6116=0. The equation whose roots are tan2⁡θ and cot2⁡θ is

cos2⁡θ+b+sin2⁡θ+b=−4⇒b=−52cos2⁡θ+bsin2⁡θ+b=6116⇒ cos2⁡θsin2⁡θ+b+b2=6116⇒ cos2⁡θsin2⁡θ=6116+52−254=6116−154=116 Sum of roots =tan2⁡θ+cot2⁡θ=1−2sin2⁡θcos2⁡θsin2⁡θcos2⁡θ=1−18116=14Product of roots = 1