Question

Prove that:
$\frac{cos \alpha }{1 - tan \alpha } - \frac{sin \alpha }{1 + cot \alpha } = cos \alpha - sin \alpha$
​

Answer 1

Step-by-step explanation:

cosA/1+tanA - sinA/1+cotA

=cos²A/cosA+sinA - sin²A/sinA+cosA

=cos²A-sin²A/cosA+sinA

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

=cosA-sinA