Question

Упростите выражение ctg (pi/2 + 5x) + ctg (pi-5x) + 1-cos^2x/(1-sin^2x)

Answer 1

1)$ctg( \frac{ \pi }{2} + 5x) + ctg( \pi -5x) + 1 - \frac{Cos ^{2}x }{1-Sin ^{2}x } = - tg5x- ctg5x+1- \frac{Cos ^{2}x }{Cos ^{2}x }$$= - tg5x - ctg5x+1-1 = - (tg5x + \frac{1}{tg5x}) = - \frac{tg ^{2}5x+1 }{tg5x}$$= - \frac{ \frac{1}{Cos ^{2}5x } }{ \frac{Sin5x}{Cos5x} } =- \frac{1*Cos5x}{Cos ^{2}5x* Sin5x } - \frac{1}{Cos5x* Sin5x} =- \frac{2}{Sin10x}$