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Question Number 200788 by hardmath last updated on 23/Nov/23

sinx   +   cosx   =   tgx  x = ?

$$\mathrm{sin}\boldsymbol{\mathrm{x}}\:\:\:+\:\:\:\mathrm{cos}\boldsymbol{\mathrm{x}}\:\:\:=\:\:\:\mathrm{tg}\boldsymbol{\mathrm{x}} \\ $$$$\mathrm{x}\:=\:? \\ $$

Answered by Frix last updated on 23/Nov/23

x=2tan^(−1)  t leads to  t^4 −4t^3 −2t^2 +1=0  No nice solution.  t_1 ≈.513620  t_2 ≈4.43911  x_1 ≈.948968+2nπ  x_2 =2.69845+2nπ

$${x}=\mathrm{2tan}^{−\mathrm{1}} \:{t}\:\mathrm{leads}\:\mathrm{to} \\ $$$${t}^{\mathrm{4}} −\mathrm{4}{t}^{\mathrm{3}} −\mathrm{2}{t}^{\mathrm{2}} +\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{No}\:\mathrm{nice}\:\mathrm{solution}. \\ $$$${t}_{\mathrm{1}} \approx.\mathrm{513620} \\ $$$${t}_{\mathrm{2}} \approx\mathrm{4}.\mathrm{43911} \\ $$$${x}_{\mathrm{1}} \approx.\mathrm{948968}+\mathrm{2}{n}\pi \\ $$$${x}_{\mathrm{2}} =\mathrm{2}.\mathrm{69845}+\mathrm{2}{n}\pi \\ $$

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