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)
$sin( - 225) = - sin225 = -sin(180 + 45) = - ( - sin45) = sin45 = frac{ sqrt{2} }{2}$