Question

solve this if you can do it. don't give meaningless answers.​

Answer 1

Step-by-step explanation:

Answer 2

Answer:

your solution is as follows

pls mark it as brainliest

Step-by-step explanation:

$to \: find : \\ \: \frac{1}{tan \: x} + \frac{sin \: x}{1 + cos \: x} \\ \\ given \: that \\ 1 + cot {}^{2} x = ( \sqrt{3 + 2 \sqrt{2} - 1 } \: ) {}^{2} \\ \\ cosec {}^{2} x = ( \sqrt{3 + 2 \sqrt{2} - 1} \: ) {}^{2} \\ \\ cosec \: x = \sqrt{3 + 2 \sqrt{2} - 1 } \\ \\ now \: given \: expression \: can \: \: be \\ written \: as \\ \\ \frac{1}{tan \: x} + \frac{sin \: x}{1 + cos \: x} \\ \\ = \frac{1}{tan \: x} + \frac{sin \: x}{1 + cos \: x} \times \frac{1 - cos \: x}{1 - cos \: x} \\ \\ = cot \: x + \frac{sin \: x(1 - cos \: x)}{1 - cos {}^{2} \: x } \\ \\ = cot \: x + \frac{sin \: x(1 - cos \: x)}{sin {}^{2} x} \\ \\ = cot \: x + \frac{1 - cos \: x}{sin \: x} \\ \\ = cot \: x + \frac{1}{sin \: x} - \frac{cos \: x}{sin \: x} \\ \\ = cot \: x + cosec \: x - cot \: x \\ \\ = cosec \: x \\ \\ = \sqrt{3 + 2 \sqrt{2} - 1}$