= (tgacosa)^2 + (ctgasina)^2

Multiplying out both terms, we get:

= tga^2 cosa^2 + ctga^2 sina^2

Since tga and ctga are reciprocals of each other, we can substitute tga = 1/ctga into the equation:

= (1/ctga)^2 cosa^2 + ctga^2 sina^2

= cosa^2/ctga^2 + ctga^2 * sina^2

= cosa^2/cosa^2 + sina^2

= 1 + sina^2

Therefore, (tgacosa)^2 + (ctgasina)^2 simplifies to 1 + sina^2.