Question

Prove the identity: one plus tan theta by one plus cot theta equals tan theta

Answer 1

$\frac{1 + tan \theta}{1 + cot \theta} \\ = \frac{1 + \frac{sin \theta}{cos \theta} }{1 + \frac{cos \theta}{sin \theta} } \\ = \frac{cos \theta + sin \theta}{cos \theta} \times \frac{sin \theta}{sin \theta + cos \theta} \\ = \frac{sin \theta}{cos \theta} \\ = tan \theta$