Question

prove:-

sin theta/cot theta + cosec theta = 2 + sin theta/cot theta - cosec theta

pls solve this.​

Answer 1

Answer:

I think it help you dear .

Answer 2

Answer:

your proof is as follows

pls mark it as brainliest

Step-by-step explanation:

$to \: prove : \\ \frac{sin \: x}{cot \: x + cosec \: x} = 2 + \frac{sin \: x}{cot \: x - cosec \: x} \\ \\ \frac{sin \: x}{cot \: x + cosec \: x} - \frac{sin \: x}{cot \: x - cosec \: x} = 2 \\ \\ LHS = \frac{sin \: x}{cot \: x + cosec \: x} - \frac{sin \: x}{cot \: x - cosec \: x} \\ \\ = \frac{sin \: x(cot \: x - cosec \: x) - sin \: x(cot \: x + cosec \: x)}{(cot \: x + cosec \: x)(cot \: x - cosec \: x)} \\ \\ = \frac{sin \: x.cot \: x - sin \: x.cosec \: x - sin \: x.cot \: x - sin \: x.cosec \: x}{cot {}^{2} \: x - cosec {}^{2} \: x} \\ \\ = \frac{ - 2.sin \: x.cosec \: x}{ - 1} \\ \\ = \frac{ - 2(1)}{ - 1} \\ \\ = 2 \\ \\ = RHS \\ \\ thus \: proved$