Statement-1: Every function can be uniquely expressed as the sum of an even function and an odd function. Statement-2: The set of values of parameter a for which the functions f(x) defined as ` f(x)=tan(sinx)+[(x^(2))/(a)]` on the set [-3,3] is an odd function is , `[9,oo)`A. Statement-1 is True, Statement-2 is True, statement-2 is a correct explanation for the statement-1 .B. Statement-1 is True, Statement-2 is True, statement-2 is not a correct explanation for the statement-1 .C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False , Statement-2 is True.

Statement-1: Every function can be uniquely expressed as the sum of an

1.	Statement-1: Every function can be uniquely expressed as the sum of an even function and an odd function. Statement-2: The set of values of parameter a for which the functions f(x) defined as ` f(x)=tan(sinx)+[(x^(2))/(a)]` on the set [-3,3] is an odd function is , `[9,oo)`A. Statement-1 is True, Statement-2 is True, statement-2 is a correct explanation for the statement-1 .B. Statement-1 is True, Statement-2 is True, statement-2 is not a correct explanation for the statement-1 .C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False , Statement-2 is True.
Answer» Correct Answer - B Clearly , statement-1 is true .(see theory ) It is given that `f(x)=tan(sinx)+[(x^(2))/(a)]` is an odd function. `:.f(-x)=-f(x)` `implies -tan (sinx)+[(x^(2))/(a)]=-tan(sinx)-[(x^(2))/(a)]` `implies 2[(x^(2))/(a)=0` `implies 0le (x^(2))/(a) lt 1` `implies a gt 0 and 0 lex^(2) lt a " for all " x in[-3,3]` `implies a gt 9, i.e., a in [9,oo)` so, statement-2 is also true.

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