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`        find the most general solutions for 2sin x + 2cos x = 21 - (2)-1/2`
7 years ago

147 Points
```										Dear
2sin x + 2cos x = 21 - (2)-1/2

As we know AM ≥GM
(2sin x + 2cos x)/2≥(2sin  x  2cos x )1/2    equality occur when 2sin  x = 2cos x
or   (2sin  x + 2cos x)/2≥(2sin   x +cosx )1/2
mimimum value occur sinx+cosx=-√2
or   (2sin   x + 2cos x)/2≥(2-√2 )1/2
or   (2sin    x + 2cos x)≥21-1/√2
so for solution equality should be occur
ie    2sin  x = 2cos x
sinx =cosx
tanx =1
x=n∏ +∏/4
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```
7 years ago
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