Trig Proof: Prove(cosB/1-tanB) + (sinB/1-cotB) = sinB + cosB

[LMcKendry]

I'm having problems solving this proof. Can anyone help?

Prove that (cosB/1-tanB) + (sinB/1-cotB) = sinB + cosB

 

[o_O]

Try starting off with converting everything on the left side into terms of sinB and cosB and combine the fractions:

\(\displaystyle \L\frac{cos B}{1 - tanB} + \frac{sinB}{1-cotB}\)

\(\displaystyle \L= \frac{cosB}{\frac{cosB}{cosB} - \frac{sinB}{cosB}} + \frac{sinB}{\frac{sinB}{sinB} - \frac{cosB}{sinB}}\)

etc. etc.