Question

if cosecA +cotA=k then prove cosA k*2-1/k*2-1

Answer 1

we know according to trigonometric formula
cosec^2A-cot^2A=1
(cosecA+cotA)(cosecA-cotA)=1
cosecA-cotA=1/k------(1)
and question given
cosecA+cotA=k-------(2)
solve this
then we find
cosecA=(k^2+1) /2k
hence cosA=(k^2-1)/(k^2+1)