Question

Prove that 1+cosA-sin^2A/sinA(1+cosA)=cot A​

Answer 1

Step-by-step explanation:

$\frac{1 + cos \theta - {sin}^{2} \theta}{sin \theta(1 + cos \theta)} = cot \theta \\ LHS = \frac{1 + cos \theta - {sin}^{2} \theta}{sin \theta(1 + cos \theta)} \\ = \frac{1 + cos \theta - (1 - {cos}^{2} \theta)}{sin \theta(1 + cos \theta)} \\ = \frac{1 + cos \theta - 1 + {cos}^{2} \theta}{sin \theta(1 + cos \theta)} \\ = \frac{cos \theta + {cos}^{2} \theta}{sin \theta(1 + cos \theta)} \\ = \frac{cos\theta (1 + {cos} \theta)}{sin \theta(1 + cos \theta)}\\ = \frac{cos\theta }{sin \theta} \\ = cot\theta \\ RHS \:$

Thus proved: