If f (x) = asin (x + π / 4) + bcos (x - π / 4) (AB is not equal to 0 and is even function, then the pair of ordinal numbers (a, b) can be -- (one of them) | Math enthusiast | Mathematical art

If f (x) = asin (x + π / 4) + bcos (x - π / 4) (AB is not equal to 0 and is even function, then the pair of ordinal numbers (a, b) can be -- (one of them)

F (x) = asin (x + π / 4) + bcos (x - π / 4) = asin (x + π / 4) + bsin (π / 2 + X - π / 4) = asin (x + π / 4) + bsin (x + π / 4) = (a + b) sin (x + π / 4). Since sin (x + π / 4) is not an even function, if f (x) is an even function, a + B = 0 is necessary, so any one that satisfies this condition can, of course ab ≠ 0

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