The correct option is A 4cos22x+2cos2x−1=0
4cos2x+2cosx−1=0→
This is a quadratic equation in cosx and in all options given are quadratic equations are in cos2x.
Let the roots of the given equation be m and n.
Then the roots of the required equation be 2m2−1 and 2n2−1 as cos2x=2cos2x−1.
Now,
4cos2x+2cosx−1=0
m+n=−12, mn=−14
Sum and product of the roots of required equation are
2(m2+n2)−2=2[(m+n)2−2mn]−2=−12
Similarly,
(2m2−1)(2n2−1)=4m2n2−2(m2+n2)+1=−14
Therefore, required equations are
4cos22x+2cos2x−1=0