Udowodnij tożsamości trygonometryczne : a). (sin alfa + cos alfa)^2 + (sin alfa - cos alfa)^2 =2 b). tg alfa - ctg alfa = (tg alfa -1) (ctg alfa +1)
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( sin a + cos a )^2 + ( sin a - cos a )^2 = sin^2 a + 2sin a * cos a + cos^2 a + sin^2 a - 2cos a * sin a + cos^2 a = 2 ( sin ^2 a + cos^2 a ) = 2*1 = 2
b) tg a - ctg a = tg a * ctg a + tg a - ctg a - 1
tg a - ctg a = tg a - ctg a + 1 - 1
tg a - ctg a = tg a - ctg a
a) L= sin^a + 2sinacosa + cos^2a + sin^2 - 2sinacosa+cos^2a = 2(sin^2a +cos^2a)= 2 *1 = 2
P =2
L=P
c.k.d
b) P= tgactga+ tga -ctga -1 = 1+tga-ctga -1 = tga-ctga
L= tga- ctga
P= L
c.k.d