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Question Number 157044 by MathSh last updated on 18/Oct/21

$$\mathrm{Solve}\mathrm{for}\mathrm{real}\mathrm{numbers}:$$ $$(\sin 2\mathbf{x}+{4\cos }^2\mathbf{x}+1)(\cos 5\mathbf{x}-\cos \mathbf{x})<0$$

Answered by mindispower last updated on 19/Oct/21

$$1+sin\left(2x\right)={(sin\left(x\right)+cos\left(x\right))}^2$$ $$\iff ({(sin\left(x\right)+cos\left(x\right))}^2+4{cos}^2\left(x\right))⩾0$$ $$cos\left(5x\right)-cos\left(x\right)=-2\mathit{s}\mathit{i}\mathit{n}\left(3\mathit{x}\right)\mathit{s}\mathit{i}\mathit{n}\left(2\mathit{x}\right)$$ $$\iff sin\left(2x\right)sin\left(3x\right)>0$$ $$nothardstarther$$

Commented byMathSh last updated on 19/Oct/21

$$\mathrm{Very}\mathrm{nice}\mathrm{dear}\mathrm{Ser}\mathrm{thank}\mathrm{you}$$

Commented bymindispower last updated on 19/Oct/21

$$withepleasur$$

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