Question

cot A-1/
2-sec A =
cot A/
1+tan A​

Answer 1

LHS = (CotA -1) /( 2- Sec²A )

= ( CotA-1) / (1 + 1 - Sec²A)

= (1/tanA)-1 / ( 1 - tan²A) ●Since tan²A +1 = sec²A So, 1- Sec²A = - tan²A

= (1-tanA) / tanA (1+tanA)(1-tanA) ● by identity a² -b² = (a+b) ( a-b)

= 1/ tanA(1+tanA)

= CotA / (1+tanA) = RHS

[ Hence Proved]