Equation sin^4x + cos^4x + sin 2x +...
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Equation ( sin ^{4} x+cos ^{4} x+sin 2 x+k=0 ) must have real solutions if
(A) ( k=0 )
(B) ( |k| leq frac{1}{2} )
(C) ( -frac{3}{2} leq k leq frac{1}{2} )
(D) ( -frac{1}{2} leq k leq frac{3}{2} )

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Maths
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Equation sin^4x + cos^4x + sin 2x + k = 0 must have real solutions if
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( sin ^{4} x+cos ^{4} x+sin 2 x+k=0 )
( Rightarrow quadleft(sin ^{2} x+cos ^{2} xright)^{2}-2 sin ^{2} x cos ^{2} x+sin 2 x+k=0 )
( Rightarrow frac{1-sin ^{2} 2 x}{2}+sin 2 x+k=0 )
( Rightarrow quad-2 leqslant sin 2 x-1 leqslant 0 Rightarrow 0 leqslant(sin 2 x-1)^{2} leq 4 )
( Rightarrow quad 0 leqslant frac{(sin 2 x-1)^{2}}{2} leqslant 2 )
( Rightarrow quad frac{-3}{2} leq frac{(sin 2 x-1)^{2}}{2}-frac{3}{2} leq frac{1}{2} )
( Rightarrow quad frac{-3}{2} leqslant k leqslant frac{1}{2} )
Option (c)

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