cotx tanx=1

Question

verify each identity

Answer 1

In a right triangle tan(x)=opposite/adjacent (where x is one of the angles other than the right angle).

cot(x)=adjacent/opposite, so:

 cot(x)tan(x)=(adjacent/opposite)(opposite/adjacent)=1.

If the two non-right angles are x and y it's clear that tan(x)=cot(y) and cot(x)=tan(y), x+y=90°.