Question

Show that: 

`sqrt((1-cos"A")/(1+cos"A"))=cos"ecA - cotA"`

Answer 1

LHS = `sqrt((1-cos"A")/(1+cos"A"))`

 

⇒ LHS = `sqrt((1-cos"A")/(1+cos"A")xx (1-cos"A")/(1-cos"A"))`

 

⇒ LHS = `sqrt(((1-cos"A")^2)/(1-cos^2"A"))`

 

=`sqrt(((1-cos"A")^2)/sin^2"A")`  ....(sin²A =1- cos²A)

 

⇒ LHS = `sqrt(((1-cos"A")/sin"A")^2)`

 

⇒ LHS = `(1-cos"A")/sin"A" = 1/sin"A" + cos"A"/sin"A"`

 

⇒ LHS = `cos"ecA"-cot"A"` = RHS

Hence Proved