1)... lim (x→0) [ sin ( π cos² x ) ] / x²

= lim (x→0) { sin [ π ( 1 - sin² x ) ] } / x²

= lim (x→0) [ sin ( π - π sin² x ) ] / x²

= lim (x→0) [ sin ( π sin² x ) / x²

= lim (x→0) [ ( π sin² x ) / x² ] ....................... from (1)

= π • [ lim (x→0) ( (sin x) / x ) ]²

= π • [ 1 ]²

= π ........................................... Ans.

astha

8 Years agoGrade 12th pass