Therefore, cos/(1-tan) + sin/(1-cot) = sin + cos

[Miike012]

Trig Question...

Homework Statement

Prove: cos/(1-tan) + sin/(1-cot) = sin + cos

The Attempt at a Solution

Cos/(1-sin/cos) + sin/(1 - cos/sin)

cos/((cos-sin)/cos) + sin/ ((sin - cos)/sin)

cos^2/(cos-sin) +sin^2/(sin-cos)

(cos - sin)(cos+sin)/(cos - sin)^2

(cos + sin)/(cos - sin)

 

[symbolipoint]

I believe you can manage differently from this step:

cos^2/(cos-sin) +sin^2/(sin-cos)

I have not tried the identity yet. From the step I quoted, you may be able to use cos-sin = -(sin-cos). Try it and see if it allows you something more effective.

 

[Miike012]

yes it works... it becomes (sin^2 - cos^2)/(sin -cos)

(sin - cos)(sin + cos)/(sin-cos)
sin + cos