sprawdź czy podana równość jest tożsamością trygonometryczną
[/tex]
sinx/(1+cos x) + (1+cos x)/ sin x= 2/ sin x
[ sin ²x+(1+cos x)²]/ [sin x(1+cos x)]=2/sin x
[ sin²x+1+2 cos x+cos ²x]/[sin x(1+cos x)]=2/sin x
[2+2cos x]/[sin x(1+cos x)]=2/sin x
[2(1+cos x)]/[sin x (1+cos x)]=2/sin x
2/sin x=2/sin x
tak, to tożsamośc
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[/tex]
sinx/(1+cos x) + (1+cos x)/ sin x= 2/ sin x
[ sin ²x+(1+cos x)²]/ [sin x(1+cos x)]=2/sin x
[ sin²x+1+2 cos x+cos ²x]/[sin x(1+cos x)]=2/sin x
[2+2cos x]/[sin x(1+cos x)]=2/sin x
[2(1+cos x)]/[sin x (1+cos x)]=2/sin x
2/sin x=2/sin x
tak, to tożsamośc