If ( sin ⁡x- cos^2 ⁡x) (3-3 sin ⁡x+ sin^2 ⁡x)+4 | sin ⁡x-1 |, then x=

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Accepted Answer

Correct answer: A. (a) Given ( sin ⁡x- cos^2 ⁡x) (3-3 sin ⁡x+ sin^2 ⁡x)+4 | sin ⁡x-1 | ( sin^2 ⁡x+ sin ⁡x-1) ( sin^2 ⁡x-3 sin ⁡x+3) (( sin^2 ⁡x-3 sin ⁡x+3)+ (4 sin ⁡x-4 )) ( sin^2 ⁡x-3 sin ⁡x+3)+ |4 sin ⁡x-4 | If |a+b | |a |+ |b | ab 0 ( sin^2 ⁡x-3 sin ⁡x+3) (4 sin ⁡x-4 ) 0 sin^2 ⁡x-3 sin ⁡x+3>0 ∀x ∈R sin ⁡x-1 0 ⇒ sin ⁡x=1 ⇒x= (4n+1 ) 2 ,n ∈Z

$If (sin x - cos^{2} x) \geq (3 - 3 sin x + sin^{2} x) + 4 | sin x - 1 |, then x =$

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