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Question Number 37155 by ajfour last updated on 09/Jun/18

$$3\cos x-4\sin x=\tan {}^{2}x$$$$locatex.$$

Commented by behi83417@gmail.com last updated on 09/Jun/18

$$c=cosx,s=sinx$$$$3c-4s=\frac{s^2}{c^2}\Rightarrow 3c^3-4{sc}^2=1-c^2$$$$\Rightarrow 4{sc}^2=3c^3+c^2-1\Rightarrow 16s^2{c}^4={(3c^3+c^2-1)}^2$$$$\Rightarrow 25c^6+6c^5-15c^4-6c^3-2c^2+1=0$$$$\Rightarrow c=0.41,0.85$$$$\mathit{c}\mathit{o}\mathit{s}\mathit{x}=0.41\Rightarrow \mathit{x}=360\mathit{k}\pm 65.8^{\bullet }$$$$\mathit{c}\mathit{o}\mathit{s}\mathit{x}=0.85\Rightarrow \mathit{x}=360\mathit{l}\pm 31.8^{\bullet }.◼$$$$$$

Commented by ajfour last updated on 10/Jun/18

$$thankyouSir.(iscalculatormust?)$$

Commented by MJS last updated on 10/Jun/18

$$\mathrm{I}\mathrm{think}\mathrm{so}$$$$\mathrm{I}\mathrm{tried}\mathrm{to}\mathrm{set}\cos x=\sqrt{1-{\sin }^{2}x}\mathrm{and}\mathrm{vice}\mathrm{versa}$$$$\mathrm{and}\mathrm{it}\mathrm{always}\mathrm{leads}\mathrm{to}\mathrm{a}\mathrm{polynome}\mathrm{of}\mathrm{degree}6$$

Commented by ajfour last updated on 10/Jun/18

$$SirpleaseattemptQ.37166also.$$

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