JEE Main 2016 · 9 Apr · Shift 1, Mathematics question 88

With $c=\cos^2x$ the expression is $\left|\sqrt{2c^2+14c+2}-\sqrt{2c^2-18c+18}\right|$, which grows steadily from 0 at $c=\frac12$ to $2\sqrt2$ at c = 0 or 1. It equals 1 at two values of c strictly between 0 and 1, and each gives four x in $[0,2\pi]$: 8 solutions.