Question

Przekształcanie wyrażeń trygonometrycznych

Answer 1

Odpowiedź:

Szczegółowe wyjaśnienie:

a.

sinα*cos(90'-α)+cos(-α)*sin(90'+α)=sinα*sinα+cosα*cosα=sin²α+cos²α=1

b.

sin(180'-α)*sinα-sin(-α)*cos(180'+α)=sinα*sinα+sinα*(-cosα)=sin²α-sinαcosα

c.

sin(90'-α)*sin(90'+α)+sin(180'+α)*cos(90'+α)=cosα*cosα-sinα*(-sinα)=

=cos²α+sin²α=1

d.

sin(90'-α)-cos(180'-α)+tg(180-α)-ctg(270'+α)=cosα+cosα-tgα+tgα=

=2cosα

e.

sin²(180'-α)+tg²(180'-α)*tg²(270'+α)+sin(90'+α)*cos(α-360')=

=(sinα)²+(-tgα)²*(-ctgα)²+cosα*cosα=sin²α+(tgα)²*(ctgα)²+cos²α=1+(tgα*ctgα)²=1+1²=2