Question

fie a=pi -arcsin 3/5 Calculati cos a+5cos2a

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Answer 1

$\it cos(\pi-t)=-cost \\ \\ cos a =cos(\pi-arcsin\dfrac{3}{5})=-cos\Big (arcsin\dfrac{3}{5}\Big )=-\dfrac{3}{5}\\ \\ \\ cos2a=2cos^2a-1 =2\cdot\Big(-\dfrac{3}{5}\Big )^2-1=2\cdot\dfrac{9}{25}-1=\dfrac{18}{25}-1=-\dfrac{7}{25}\\ \\ \\ coa a+5cos 2a=-\dfrac{3}{5}+5\cdot\Big (-\dfrac{7}{25}\Big) = -\dfrac{3}{5}-\dfrac{7}{5} = -\dfrac{10}{5}=-2$