Question

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IF KNOWN YHEN ANSWER PLZZ..

Let f(x) = sin 3
x
+ cos
10

3x
for all real x. Find the least natural number n such that f(n + x) = f(x) for all real x.​

Answer 1

$\boxed{ \huge{ \bf{ \red{Answer :}}}}$

When, f(x) = sin 3x + cos10 3x

Therefore,

Period of sin x = 2π

Period of sin 3 x = 6π

Period of cos10/3x = 3/20π

Period of f(x) = (LCM of 6π and 3/20π)

=> =3 180π

=> n = 60π

=> n = 60

$\boxed{ \sf \green{Hence, Value \: of \: n = 60}}$

Answer 2

Answer:

hope it helps you ! .......................