Question

Prove that `(cosec theta-cot theta)^2=(1-cos theta)/(1+cos theta)`

Answer 1

LHS `=("cosec"theta- cot theta)^(2)`
`=((1)/(sin theta)-(cos theta)/(sin theta))^(2)=((1-cos theta)/(sin theta))^(2)`
` = ((1-cos theta)^(2))/(sin^(2) theta)=((1-cos theta)(1-cos theta))/((1-cos^(2)theta)) " "[ because sin^(2)theta=1-cos^(2)theta]`
`=((1-cos theta)(1-cos theta))/((1+cos theta)(1-cos theta))=((1-cos theta))/((1+cos theta))= " RHS. " `
` therefore " LHS " = " RHS. " `