Question

Sin la a patra de x +cos la a patra de x =1/2

Answer 1

$sin^{4}x + cos^{4}x = \frac{1}{2} \\ ( sin^{2}x + cos^{2}x)^{2} = sin^{4}x+ cos^{4}x +2sin^{2}xcos^{2}x =\ \textgreater$[tex] \\ sin^{4} + cos^{4}= ( sin^{2}x + cos^{2}x)^{2}-2sin^{2} xcos^{2}x \\ sin^{4} + cos^{4}= 1^{2} -2sin^{2} xcos^{2}x \\ 1 -2sin^{2} xcos^{2}x = \frac{1}{2} |-1 \\ -2sin^{2} xcos^{2}x= - \frac{1}{2} |:(-2) \\ sin^{2} xcos^{2}x= 1 (*) \\ sin^{2} x= \frac{1-cos2x}{2} \\ cos^{2} x= \frac{1+cos2x}{2} \\ inlocuiesti [/tex]