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Question Number 189916 by mustafazaheen last updated on 24/Mar/23

$$\mathrm{when}\mathrm{sinx}\times \mathrm{cosx}=-\frac{1}{4}$$$$\mathrm{find}\mathrm{sinx}+\mathrm{cosx}=?$$

Answered by aminitindas last updated on 24/Mar/23

$$$$$$\mathbf{Ans}:$$$${(\sin x+\cos x)}^2={\sin }^{2}x+{\cos }^{2}x+2\sin x\cos x$$$${(\sin x+\cos x)}^2=1+2(-\frac{1}{4})=1-\frac{1}{2}=\frac{1}{2}$$$$\sin x+\cos x=\pm \frac{1}{\sqrt{2}}$$$$$$$$aminitindas,\mathrm{March}24,{}^{\prime }23$$

Answered by CElcedricjunior last updated on 26/Mar/23

$$\{\begin{array}{l}\mathit{s}\mathit{i}\mathit{n}\mathit{x}\times \mathit{c}\mathit{o}\mathit{s}\mathit{x}=-\frac{1}{4}\\ \mathit{s}\mathit{i}\mathit{n}\mathit{x}+\mathit{c}\mathit{o}\mathit{s}\mathit{x}=\mathit{k}\end{array}$$$$\mathit{c}\mathit{a}\mathit{l}\mathit{c}\mathit{u}\mathit{l}\mathit{o}\mathit{n}\mathit{s}\mathit{s}\mathit{i}\mathit{n}\mathit{x}+\mathit{c}\mathit{o}\mathit{s}\mathit{x}=\mathit{k}◼\mathit{M}oivre$$$$\mathit{o}\mathit{n}{(\mathit{c}\mathit{o}\mathit{s}\mathit{x}+\mathit{s}\mathit{i}\mathit{n}\mathit{x})}^2=1+2\mathit{s}\mathit{i}\mathit{n}\mathit{x}\mathit{c}\mathit{o}\mathit{s}\mathit{x}$$$$=\frac{1}{2}$$$$\mathit{s}\mathit{i}\mathit{n}\mathit{x}+\mathit{c}\mathit{o}\mathit{s}\mathit{x}=\mp \frac{\sqrt{2}}{2}$$$$\mathcal{L}emignonfofanacedricjunior$$$$$$

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