Question

1+costheta/sintheta - sintheta/1+costheta =2cot theta

Answer 1

$\large\red{ANSWER}$

$\frac{1 + cos \: \alpha }{sin \: \alpha } - \frac{sin \: \alpha }{1 + cos \: \alpha } = 2cot \: \alpha \\ left \: hand \: side \\ \frac{{(1 + cos \: \alpha )}^{2} \: - {sin}^{2} \alpha }{sin \: \alpha (1 + cos \: \alpha )} \\ \frac{1 + {cos}^{2} \alpha + 2cos \: \alpha - {sin}^{2} \: \alpha }{sin \: \alpha (1 + cos \: \alpha )} \\ \frac{ {cos}^{2} \alpha + {cos}^{2} \alpha + 2cos \: \alpha }{sin \: \alpha (1 + cos \: \alpha )} \\ \frac{2 {cos}^{2} \alpha + 2cos \: \alpha \: }{sin \: \alpha (1 + cos \: \alpha )} \\ \frac{2cos \: \alpha (cos \: \alpha + 1)}{sin \: \alpha (1 + cos \: \alpha )} \\ = > 2 \frac{cos \: \alpha }{sin \: \alpha } \\ = > 2cot \: \alpha \\ lhs = rhs$

$\large\blue{HENCE\:PROVED}$

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Answer 2

Step-by-step explanation:

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