express sin A(1+cot2A) in terms of cosine A?

Question

to solve such questions,one should use the reciprocal identities, pythagorean identities, and ratio identities. the number "2" found beside the word "cot" is an exponent.

Answer 1

Sin A(1+Cot^2A)
=Sin A(1+Cos^2A/Sin^2A)
=Sin A[(Sin^2A+Cos^2A)/Sin^2A]
=Sin A(1/Sin^2A)=1/Sin A=1/(1-Cos^2A)^1/2

Answer 2

sin A (1 + cot^2 A)
= sin A (cosec^2 A)
= sin A / sin^2 A
= 1 / sin A
= 1 / √(1 - cos^2 A) assuming first or second quadrant