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Question Number 169771 by greougoury555 last updated on 08/May/22

$$\frac{1}{1+\cos {}^{2}x}+\frac{1}{\sin {}^{2}x+1}=\frac{48}{35}$$

Answered by kapoorshah last updated on 08/May/22

$$SyberMath$$

Answered by thfchristopher last updated on 08/May/22

$$\Rightarrow \frac{1+{\sin }^{2}x+1+{\cos }^{2}x}{1+{\sin }^{2}x+{\sin }^{2}x{\cos }^{2}x+{\cos }^{2}x}=\frac{48}{35}$$$$\Rightarrow \frac{3}{2+{\sin }^{2}x{\cos }^{2}x}=\frac{48}{35}$$$$\Rightarrow 105=96+{48\sin }^{2}x{\cos }^{2}x$$$$\Rightarrow {\sin }^{2}x{\cos }^{2}x=\frac{9}{48}$$$$\Rightarrow \frac{1}{4}{\sin }^{2}2x=\frac{9}{48}$$$$\Rightarrow {\sin }^{2}2x=\frac{36}{48}$$$$\Rightarrow \sin 2x=\frac{\sqrt{3}}{2}\mathrm{or}\sin 2x=-\frac{\sqrt{3}}{2}$$$$2x=n\pi \mp \frac{\pi }{3}$$$$x=\frac{n\pi }{2}\mp \frac{\pi }{6}$$

Answered by cortano1 last updated on 08/May/22

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