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Question Number 174790 by MathsFan last updated on 11/Aug/22

Commented by MathsFan last updated on 11/Aug/22

$$\mathrm{any}\mathrm{help}?$$

Answered by cortano1 last updated on 11/Aug/22

Answered by Ar Brandon last updated on 11/Aug/22

$$6.$$$$3(2\sin x-\cos x)=2(\sin x-3\cos x)$$$$6\sin x-3\cos x=2\sin x-6\cos x$$$$4\sin x=-3\cos x$$$$\tan x=-\frac{3}{4}\Rightarrow x={\tan }^{-1}(-\frac{3}{4})PV$$$$\Rightarrow x=\pi -\arctan \left(\frac{3}{4}\right)\vee x=-\arctan \left(\frac{3}{4}\right)$$

Answered by Ar Brandon last updated on 11/Aug/22

$$7.$$$$2\sin x\tan x+3=0\Rightarrow \frac{{2\sin }^{2}x}{\cos x}+3=0$$$$\Rightarrow 2(1-{\cos }^{2}x)+3\cos x=0$$$$\Rightarrow {2\cos }^{2}x-3\cos x-2=0$$$$\Rightarrow (2\cos x+1)(\cos x-2)=0$$$$\Rightarrow 2\cos x+1=0(-1⩽\cos x⩽1)$$$$\Rightarrow \cos x=-\frac{1}{2},PV=\frac{\pi }{3}$$$$\Rightarrow x=\pi -\frac{\pi }{3}=\frac{2\pi }{3},x=\pi +\frac{\pi }{3}=\frac{4\pi }{3}$$

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