JEE Main 2016 · 10 Apr · Shift 1, Mathematics question 70

$(1-\cos2x)^2=4\sin^4x\approx4x^4$. With $\tan x\approx x+\frac{x^3}3$ and $\tan2x\approx2x+\frac{8x^3}3$, the denominator is $\approx-2x^4$. The limit is −2.