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Question Number 12626 by @ANTARES_VY last updated on 27/Apr/17

$$2{\mathbf{cos}}^2\mathit{\alpha }-3\mathbf{sin}\mathit{\alpha }$$$$\mathbf{Find}\mathbf{the}\mathbf{best}\mathbf{metaphore}$$

Commented by prakash jain last updated on 27/Apr/17

$$\mathrm{Are}\mathrm{u}\mathrm{using}\mathrm{google}\mathrm{translate}?$$

Answered by ajfour last updated on 27/Apr/17

$$2-3\sin \alpha -2\sin {}^2\alpha$$$$=2-4\sin \alpha +\sin \alpha -2\sin {}^2\alpha$$$$=(1-2\sin \alpha )(\sin \alpha +2)$$$$Also$$$$=2-2[{(\sin \alpha +\frac{3}{4})}^2-\frac{9}{16}]$$$$=2+\frac{9}{8}-2{(\sin \alpha +\frac{3}{4})}^2$$$$=\frac{25}{8}-2{(\sin \alpha +\frac{3}{4})}^2.$$

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