Question

Prove the identities:
cosec A - cot A = sin A ÷ 1 + cos A​

Answer 1

Answer:

this is the answer of this question

Answer 2

$Taking \: LHS$

$cosec \: A \: - \: cot \: A \\ \\ \frac{1}{sin \:A} - \frac{cos \:A}{sin \:A} \\ \\ \frac{1 - cos \: A}{sin \: A} \\ \\ \frac{1 - cos \: A}{sin \: A} \times \frac{1 + cos \: A}{1 + cos \: A } \\ \\ (\frac{1 + cos \: A}{1 + cos \: A } \: is \: nothing \: but \: 1) \\ \\ \frac{1 - cos {}^{2} A}{sin \: A (1 + cos \: A)} \\ \\ \frac{ 1 - (1 - sin {}^{2} A)}{sin \: A (1 + cos \: A)} \\ \\ \frac{ 1 - 1 + sin {}^{2} A}{sin \: A (1 + cos \: A)} \\ \\ \frac{ sin {}^{2} A}{sin \: A (1 + cos \: A)} \\ \\ \frac{sin \: A}{1 + cos \: A }$

$HENCE \: \: \: PROVED \: \: !!!$