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Question Number 164757 by mathlove last updated on 21/Jan/22

$$\cos \alpha =\frac{2}{3}$$$$sin(\frac{\pi }{2}+\alpha )-3{sin}^2(\frac{7\pi }{2}+\alpha )-2cos(5\pi +\alpha )=?$$

Commented by blackmamba last updated on 21/Jan/22

$$\Rightarrow =\cos \alpha -3\cos {}^2\alpha +2\cos \alpha$$$$\Rightarrow =3\times \frac{2}{3}-3\times \frac{4}{9}$$$$\Rightarrow =\frac{6-4}{3}=\frac{2}{3}$$

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