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2019 Auckland Mathematical Olympiad
1
f(sin x) = sin(17x) if f(cos x) = cos(17x) (2019 Auckland MO S1)
f(sin x) = sin(17x) if f(cos x) = cos(17x) (2019 Auckland MO S1)
Source:
November 15, 2021
trigonometry
algebra
Problem Statement
Function
f
f
f
satisfies the equation
f
(
cos
x
)
=
cos
(
17
x
)
f(\cos x) = \cos (17x)
f
(
cos
x
)
=
cos
(
17
x
)
. Prove that it also satisfies the equation
f
(
sin
x
)
=
sin
(
17
x
)
f(\sin x) = \sin (17x)
f
(
sin
x
)
=
sin
(
17
x
)
.
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