2sin`2 2x = 9sin 2x - 4...

Oxxxymiron158 @Oxxxymiron158

May 2022 1 8 Report

2sin`2 2x = 9sin 2x - 4

Answers & Comments

frozensupra $2sin^{2}2x=9sin2x-4 \\ 
2sin^{2}2x-9sin2x+4=0 \\ 2t^{2} -9t+4=0 \\ D=b^{2} -4ac \\ D=9^{2}-4*2*4 =49 \\ t_{1}= \frac{-b+ \sqrt{D} }{2a} = \frac{9+7}{4}=4 \\ t_{2} = \frac{-b- \sqrt{D} }{2a}= \frac{9-7}{4}= \frac{1}{2} \\ 
sin2x= \frac{1}{2} \\ 2x=(-1)^{n} *arcsin \frac{1}{2} + \pi n \\ 2x=(-1)^{n} * \frac{ \pi }{6} + \pi n \\ x= \frac{(-1)^{n}* \frac{ \pi }{6}+ \frac{ \pi n}{2} }{2}$

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