Question

express cos A in terms of cot A

Answer 1

we know that 
$cosA = \frac{1- tan^{2}A/2 }{1+ tan^{2}A/2 } \\ cosA= \frac{1- \frac{1}{ cot^{2}A/2 } }{1+ \frac{1}{ cot^{2}A/2 } } \\ cosA= \frac{ cot^{2}A/2-1 }{ cot^{2}A/2+1 }$

Answer 2

cot A=cos A/sin A
by cross multiply
sin A cot A=cos A
cot A√1-cos ² A=cos A
squaring on both sides
cot²A(1-cos²A)=cos²A
cot²A-cot²A cos²A=cos²A
cot²A=cos²A+cot²A cos²A
cot²A=cos²A(1+cot²A)
cos²A=cot²A/1+cot²A
cosA=plus or minus√cot²A/1+cot²A