Help me prove the exponential inequality 2sin2x+2cos2x≤3 Ive

Pamela Meyer

Pamela Meyer

Answered

2022-01-17

Help me prove the exponential inequality
2sin2x+2cos2x3
Ive

Answer & Explanation

Bernard Lacey

Bernard Lacey

Expert

2022-01-16Added 30 answers

Since 2sin2x1 and 2cos2x1, then
2sin2x+2cos2x=3(2sin2x1)(2cos2x1)3
Moreover,
2sin2x+2cos2x=[(2)sin2x(2)cos2x]2+2222.
RizerMix

RizerMix

Expert

2022-01-19Added 437 answers

Rearranging the equation we have that
2t+21t=322t32t+2=0
which after factoring gets us
(2t1)(2t2)=0
This is a parabola with roots at 1 and 2 that opens upward. Therefore we have that
(2t1)(2t2)012t20t1
which immediately gives us our desired result.

alenahelenash

alenahelenash

Expert

2022-01-24Added 366 answers

I think youre

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