CosecA+cotA=k find value of cosA in terms of k?

Question

I need the solution for this CosecA+CotA=k find the value of K in terms of cosA?

Answer 1

CosecA+cotA=k

 

coces(A)=1/sin(A), So

 

1/sin(A)+cos(A)/sin(A)=k

 

(1+cos(A))/sin(A))=k

 

2cos²(A/2)/2sin(A/2)cos(A/2)=k

 

cos(A/2)/sin(A/2)=k

 

cot(A/2)=k

tan(A/2)=1/k

(1-cos(A))/(1+cos(A))=1/k^2

cos(A)=(k^2+1)/(k^2-1)