Question

Why is testcross necessary to determine genotype when an organism shows a dominant trait?

Answer 1

Test cross is the cross between an organism with unknown dominant genotype and an organism with known recessive genotype.
Since dominant trait results from a dominant allele, the test cross can determine if unknown genotype is heterozygous and homozygous dominant.

If A is dominant allele, and a is recessive allele, then AA is dominant homozygote, Aa is heterozygote, and aa is recessive homozygote.
According to the Punnett square, if all of the offspring are heterozygote (Aa), then unknown genotype is dominant homozygous (AA). If half of the offspring are heterozygote, and the other half are recessive homozygote, then the unknown genotype is heterozygote (Aa).