If u=acos2x+bsin2x+bcos2x+asin2x, find the maximum and minimum value of u2.

Duncan Reed

Duncan Reed

Answered

2022-01-26

If u=acos2x+bsin2x+bcos2x+asin2x, find the maximum and minimum value of u2.

Answer & Explanation

Devyn Figueroa

Devyn Figueroa

Expert

2022-01-27Added 10 answers

u=acos2x+bsin2x+bcos2x+asin2x
Let
p=acos2x+bsin2x
q=bcos2x+asin2x
and
u=p+q
Then u2=p+q+2pq
Now
p+q=a+b
and
pq=(a+b)24(ab)28(ab)28cos4x
If cos4x=1 then u2 is maximum and is equal to
2(a+b)
If cos4x=1 then u2 is minimum and is equal to
a+b+2ab
Armani Dyer

Armani Dyer

Expert

2022-01-28Added 10 answers

Put
1cos2x=2sin2x
1+cos2x=2cos2x

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