limx→0sin(πcos2x)x² is equal to

Let L=limx→0sin(πcos2x)x²
=limx→0sin(π(1−sin²x))x²
=limx→0sin(π−πsin²x)x²
=limx→0sin(πsin²x)x² (sin(π−θ)=sinθ)
Multiplying and dividing by πsin²x. We get,
=limx→0sin(πsin²x)πsin²x × πsin²xx²
We know that, limx→0sinxx=1
∴L=π