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Question Number 161848 by mnjuly1970 last updated on 23/Dec/21

$$$$$$\mathrm{I}ftan\left(\alpha \right)=2$$$$findthevalueof$$$$$$$$\mathrm{K}=\frac{1+sin\left(8\alpha \right)-cos\left(8\alpha \right)}{1+sin\left(8\alpha \right)+cos\left(8\alpha \right)}=?$$$$$$$$$$

Commented by cortano last updated on 23/Dec/21

$$K=\frac{2\sin {}^{2}4\alpha +\sin 8\alpha }{2\cos {}^{2}4\alpha +\sin 8\alpha }=\frac{2\sin 4\alpha (\sin 4\alpha +\cos 4\alpha )}{2\cos 4\alpha (\cos 4\alpha +\sin 4\alpha )}$$$$K=\tan 4\alpha$$$$K=\left(\frac{2\tan 2\alpha }{1-\tan 2\alpha }\right)=\frac{-\frac{8}{3}}{1-\frac{16}{9}}=\frac{-24}{-7}=\frac{24}{7}$$$$R=\tan 2\alpha =\frac{2\tan \alpha }{1-\tan {}^2\alpha }=\frac{4}{1-4}=-\frac{4}{3}$$

Commented by mnjuly1970 last updated on 23/Dec/21

$$thanksalot...$$

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