A question on range of trigonometric functions. If

ohmaig00dnessyb3

ohmaig00dnessyb3

Answered question

2022-03-17

A question on range of trigonometric functions.
If u={a2cos2α+b2sin2α}+{a2sin2α+b2cos2α}, find the difference between the maximum and minimum value of u2
I tried squaring the expression on both sides but i am ending up with some complex expression, i.e, a2+b2+2sinαcosα(a2b2)2+a2b2sin2αcos2α

Answer & Explanation

Ettrapinithr

Ettrapinithr

Beginner2022-03-18Added 7 answers

By C-S
u2=a2+b2+2(a2cos2α+b2sin2α)(b2cos2α+a2sin2α)
a2+b2+2(abcos2α+absin2α)2=a2+b2+2|ab|=(|a|+|b|)2
The equality occurs when
(acosα,bsinα)(bcosα,asinα)
which says that (|a|+|b|)2 is a minimal value.

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