Question

г.д. упростить

абв вычислить

Answer 1

г)
$\frac{ {sin}^{2} \alpha }{1 - cos \alpha } - cos \alpha = \frac{ {sin}^{2} \alpha - cos \alpha (1 - cos \alpha )}{1 - cos \alpha } = \frac{ {sin}^{2} \alpha - cos \alpha + {cos}^{2} \alpha }{1 - cos \alpha } = \frac{1 - cos \alpha }{1 - cos \alpha } = 1$
д)
$\frac{ {a}^{ - 9} }{ {a}^{ - 2} \times {a}^{ - 5} } = \frac{ {a}^{ - 9} }{ {a}^{ - 2 - 5} } = \frac{ {a}^{ - 9} }{ {a}^{ - 7} } = {a}^{ - 9 - ( - 7) = {a}^{ - 9 + 7} } = {a}^{ - 2}$
а)
$\sqrt{8} \times \sqrt{5} \times \sqrt{10} = \sqrt{8 \times 5 \times 10} = \sqrt{400} = 20$
б)
$\frac{sin(\pi + \alpha )}{sin( \frac{\pi}{2} + \alpha )} = \frac{ - sin \alpha }{cos \alpha } = - tg \alpha = - tg \frac{\pi}{4} = - 1$
в)
$sin( - 225) = - sin225 = -sin(180 + 45) = - ( - sin45) = sin45 = \frac{ \sqrt{2} }{2}$