Question

`sqrt((1 + cos "A")/(1 - cos"A"))` = cosec A + cot A हे सिद्ध करा.

Answer 1

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

= `sqrt((1 + cos "A")/(1 - cos "A") xx (1 + cos "A")/(1 + cos "A"))`   ......[छेदाचे परिमेयकरण करून]

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

= `sqrt((1 + cos "A")^2/(sin^2 "A")`    ......`[(because sin^2"A" + cos^2"A" = 1),(therefore 1 - cos^2"A" = sin^2"A")]`

= `(1 + cos"A")/"sin A"`

= `1/"sin A" + "cos A"/"sin A"`

= cosec A + cot A

= उजवी बाजू

∴ `sqrt((1 + cos "A")/(1 - cos"A"))` = cosec A + cot A