Question

Given the identity tanX=sinXcosX and the relationship between the sine and cosine of complementary angles, what is tan (90°− A)?

Answer 1

Note  tanx =    sinx / cosx.    What you typed is wrong.

For complementary Angles, that is Angles that add up to 90 degrees.
For example 60 and 30 are complementary. 20 and 70 are also complementary, same is 40 and 50. That is because they both add up to 90.

For Complementary Angles:

sinx  = cos(90 - x)
cosx  = sin(90 -x)
tanx    = cot(90 -x)
cotx    =  tan(90 -x).                              cotx =  1/tanx

Therefore tan(90-A) = cotA.