Sprawdź tożsamości: a) sin x / (1+ cos x) + (1 + cos x) / sinx = 2/sinx b) [(1- sinx)/ sinx] * [(1+ sinx)/cosx] = ctgx

a) sin x / (1+ cos x) + (1 + cos x) / sinx = 2/sinx L = sin x / (1+ cos x) + (1 + cos x) / sinx = = sin²x + (1+ cos x) ² /sinx(1 + cos x) = = sin²x + 1 +2cosx + cos²x / sinx(1 + cos x) = = 2 + 2cosx /sinx(1 + cos x) = = 2(1 + cosx) / sinx(1 + cos x) = = 2/sinx = P b) [(1- sinx)/ sinx] * [(1+ sinx)/cosx] = ctgx L = [(1- sinx)/ sinx] * [(1+ sinx)/cosx] = = 1 - sin²x / sinx*cosx = = cos²x / sinx*cosx = = cosx / sinx = = ctgx = P