# Math Help - proving identities

1. ## proving identities

please i need help with this problem.

cosB/1-tanB + sinB/1-cotB = sinB + cosB

how can i prove this identity?

2. Originally Posted by Cooks
please i need help with this problem.

cosB/1-tanB + sinB/1-cotB = sinB + cosB

how can i prove this identity?
working on the left side ...

$\frac{\cos{\beta}}{\cos{\beta}} \cdot \frac{\cos{\beta}}{1-\tan{\beta}} + \frac{\sin{\beta}}{\sin{\beta}} \cdot \frac{\sin{\beta}}{1-\cot{\beta}}$

$\frac{\cos^2{\beta}}{\cos{\beta} - \sin{\beta}} + \frac{\sin^2{\beta}}{\sin{\beta}-\cos{\beta}}$

$\frac{\cos^2{\beta}}{\cos{\beta} - \sin{\beta}} - \frac{\sin^2{\beta}}{\cos{\beta} - \sin{\beta}}$

$\frac{\cos^2{\beta}-\sin^2{\beta}}{\cos{\beta} - \sin{\beta}}$

factor the numerator and finish it up ...

3. Originally Posted by Cooks
please i need help with this problem.

cosB/1-tanB + sinB/1-cotB = sinB + cosB

how can i prove this identity?
hi all