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Question Number 155878 by mnjuly1970 last updated on 05/Oct/21

$$$$$$theequationof:$$$$(a+sin\left(x\right))(a+cos\left(x\right))=a$$$$hassolutionin\mathbb{R}$$$$hence:$$$$a\in ?$$$$$$$$$$$$$$

Answered by MJS_new last updated on 05/Oct/21

$$\mathrm{solve}\mathrm{it}\mathrm{for}a\mathrm{and}\mathrm{then}\mathrm{find}\mathrm{the}\mathrm{range}:$$$$1-\sqrt{2}⩽a⩽\frac{1+\sqrt{2}+\sqrt{1+2\sqrt{2}}}{2}$$

Commented by talminator2856791 last updated on 05/Oct/21

$$\mathrm{did}\mathrm{you}\mathrm{also}\mathrm{use}\mathrm{wolframalpha}?$$

Commented by MJS_new last updated on 05/Oct/21

$$\mathrm{no}.\mathrm{I}\mathrm{used}\mathrm{my}\mathrm{own}\mathrm{brain}.$$

Answered by talminator2856791 last updated on 05/Oct/21

$$a\in (1-\sqrt{2},\frac{1}{2}+\frac{1}{\sqrt{2}}-\frac{1}{2}\sqrt{1+2\sqrt{2}})$$

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