If f : [ − 20 , 20 ] → R defined by f ( x ) = [ a π 2 ] sin x + cos x is an even function, then the set of values of ' a ' is, Where [.] is G.I.F.

Question

If f : [ − 20 , 20 ] → R defined by f ( x ) = [ a π 2 ​ ] sin x + cos x is an even function, then the set of values of ' a ' is, Where [.] is G.I.F.

TestHub · Accepted Answer

⇒ [ a x 2 ​ ] = a ⇒ 0 ≤ a x 2 ​ < 1 ⇒ a > x 2 ⇒ a > 400 ( since − 20 ≤ x ≤ 20 ) ∴ a ∈ ( 400 , ∞ ) . ]

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