Question

помогите решить .....................

Answer 1

$\sin \alpha=\dfrac{\sin \alpha}{1} =\dfrac{2\sin\frac{\alpha}{2}\cos\frac{\alpha}{2}}{\cos^2\frac{\alpha}{2}+\sin^2\frac{\alpha}{2}}=\dfrac{2\mathrm{tg}\frac{\alpha}{2}}{1+\mathrm{tg}^2\frac{\alpha}{2}}=\dfrac{2\cdot0.5}{1+0.5^2}=\dfrac{1}{1.25}=0.8$

$\cos \alpha=\dfrac{\cos \alpha}{1} =\dfrac{\cos^2\frac{\alpha}{2}-\sin^2\frac{\alpha}{2}}{\cos^2\frac{\alpha}{2}+\sin^2\frac{\alpha}{2}}=\dfrac{1-\mathrm{tg}^2\frac{\alpha}{2}}{1+\mathrm{tg}^2\frac{\alpha}{2}}=\dfrac{1-0.5^2}{1+0.5^2}=\dfrac{0.75}{1.25}=0.6$

$\mathrm{tg}\alpha =\dfrac{\sin\alpha }{\cos\alpha } =\dfrac{0.8}{0.6} =\dfrac{4}{3}$