Question

1
Prove that
1: sin/1-cot + cos/1-tan=cos+sin​

Answer 1

have:

`(sin)/(1-cot)+(cos)/(1-tan)\\\\=(sin)/(1-(cos)/(sin) )+(cos)/(1-(sin)/(cos) )\\\\=(sin^(2) )/(sin-cos)+(cos^(2) )/(cos-sin) \\\\=(sin^(2) )/(sin-cos)-(cos^(2) )/(cos-sin)\\\\=(sin^(2)-cos^(2) )/(sin - cos)\\\\=((sin-cos)(sin+cos))/(sin-cos)\\\\=sin+cos`

Explanation: