Can you solve this function problem
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Can you solve this function problem

[From: ] [author: ] [Date: 12-06-26] [Hit: ]
......
if f(x)=1-sin 2x show that:
a.) f(45+x)+f(45-x)=2(1-cos2x)
b.)f(45+x)-f(45-x)=0

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Just recall:
sin(90+θ) = cos(θ)
cos(−θ) = cos(θ)

a)

f(45+x) + f(45−x)
= 1 − sin(90+2x) + 1 − sin(90−2x)
= 2 − cos(2x) − cos(−2x)
= 2 − cos(2x) − cos(2x)
= 2 − 2 cos(2x)
= 2 (1 − cos(2x))

b)

f(45+x) − f(45−x)
= (1 − sin(90+2x)) − (1 − sin(90−2x))
= 1 − sin(90+2x) − 1 + sin(90−2x)
= 0 − cos(2x) + cos(−2x)
= −cos(2x) + cos(2x)
= 0
1
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