Question

Sprawdź czy tożsamość jest prawdziwa

Answer 1

1)

L = 1 + ctg ^2 x = 1 + [ cos x /sin x ]^2 = sin^2 x /sin ^2 x + cos^2 x /sin^2 x

= [ sin^2 x + cos ^2 x ]/ sin ^2 x = 1 / sin^2 x = P

Tak

2)

L = ctg x + sin x /[1 + cos^2 x] = cos x / sin x  + sin x / [ 1 + cos^2 x ] =

= [ cos x *(1 + cos^2 x) + sin^2 x]/[ sin x*( 1 + cos ^2 x)] =

= [ cos x + cos ^3 x + sin^2 x ]/[ sin x *( 1 + cos ^ 2 x )] =

Nie

c)

L  = cos x - tg x = cos x - sin x / cos x = cos^2 x / cos x - sin x / cos x =

= [ cos ^2 x - sin x]/cos x =

Nie