Question

How do you prove `(cotA-1)/(cotA+1) = (cosA-sinA)/(cosA+sinA)`?

Answer 1

Please refer to the Explanation.

Explanation:

`(cotA-1)/(cotA+1)`,

`={cosA/sinA-1}-:{cosA/sinA+1}`,

`={(cosA-sinA)/cancelsinA}-:{(cosA+sinA)/cancelsinA}`,

`=(cosA-sinA)/(cosA+sinA)`, as desired!

Answer 2

See below.

Explanation:

`LHS=(cotA-1)/(cotA+1)`

`=(cosA/sinA-1)/(cosA/sinA+1)`

`=(cosA/sinA-1)/(cosA/sinA+1)timessinA/sinA`

`=(cosA-sinA)/(cosA+sinA)`

`=RHS`

Answer 3

Refer to explanation.

Explanation:

**Starting from `color(red)(LHS)` **

`(cot A - 1)/(cotA+1)`

`rArr (cosA/sin A -1)/(cosA/sinA + 1)`

Since, `cotA= cosA/sin A`

`rArr ((cosA-sinA)/sinA)/((cosA+sinA)/sinA)`

`rArr((cosA-sinA)/cancelsinA)/((cosA+sinA)/cancelsinA)`

`rArr (cosA-sinA)/(cosA+sinA)`

We get `color(red)(RHS).`

`color(white)(aaaaaaaaaaaaaaaaaaaaàaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaasasaaaaaaaasaaaaaaaaaaaaaaaaa)`
Hope this helps :)