Question

Log5tg36°+log5tg54° вычислить

Answer 1

Объяснение:

$log_5tg36^0+log_5tg54^0=log_5(tg36^0*tg54^0)=log_5\frac{sin36^0*sin54^0}{cos34^0*cos54^0}=\\ log_5\frac{\frac{1}{2}*((cos(36^0-54^0)-cos(36^0+54^0)) }{\frac{1}{2}*((cos(36^0-54^0)-cos(36^0+54^0))} =log_5\frac{cos(-18^0)-cos90^0}{cos(-18^0)+cos90^0}= \\=log_5\frac{cos(18^0-0)}{cos(18^0+0)}=log_5\frac{cos18^0}{cos18^0} =log_51=0.$