Question

Udowodnij 2 tożsamości trygonometryczne



1
cosx/(1+tg x) + sinx/(1+ctg x) = 1/sinx+cosx


2.
tg ^2x - sin^2x = tg^2x × sin ^2x

Answer 1

Tg ^2x - sin^2x = tg^2x × sin ^2x
L = tg^2x - sin^2x =
= sin^2x/cos^2x - sin^2x =
= sin^2x - sin^2xcos^2x/cos^2x =
= sin^2x(1-cos^2x)/cos^2x =
= sin^2x * sin^2x / cos^2x =
= sin^4x/cos^2x =
= sin^2x/cos^2x * sin^2x =
= tg^2xsin^2x = P

L = P
:)