Question

Please someone solve this urgently...
(will mark the best answer as brainliest)

Answer 1

Answer:

your solution is as follows

pls mark it as brainliest

Step-by-step explanation:

$to \: find : value \: of \: \\ (1 + tan \: x + sec \: x)(1 + cot \: x - cosec \: x) \\ \\ = (1 + tan \: x + sec \: x)(1 + cot \: x - cosec \: x) \\ \\ = (1 + \frac{sin \: x}{cos \: x} + \frac{1}{cos \: x} )(1 + \frac{cos \: x}{sin \: x } - \frac{1}{sin \: x} ) \\ \\ = (1 + \frac{1 + sin \: x}{cos \: x} )(1 + \frac{cos \: x - 1}{sin \: x} ) \\ \\ = ( \frac{sin \: x + cos \: x + 1}{cos \: x} )( \frac{sin \: x + cos \: x - 1}{sin \: x} ) \\ \\ = ( \frac{a + b + c}{b} )( \frac{a + b - c}{a} ) \\ \\ = \frac{a {}^{2} + b {}^{2} - c {}^{2} + 2ab}{ab} \\ \\ = \frac{sin {}^{2} \: x + cos {}^{2} \: x - 1 + 2.sin \: x.cos \: x}{sin \: x.cos \: x} \\ \\ = \frac{1 - 1 + 2.sin \: x.cos \: x}{sin \: x.cos \: x} \\ \\ = \frac{2.sin \: x.cos \: x}{sin \: x.cos \: x} \\ \\ = 2$