Question

prove that (1+tan theta +sec theta) (1+cot theta -cosec theta) =2

Answer 1

Hope this helps u bro

Answer 2

$(1 + tan \theta + sec \theta)(1 + cot \theta - cosec \theta) \\ \\ = ( \frac{cos \theta + sin \theta + 1}{cos \theta} )( \frac{sin \theta + cos \theta - 1}{sin \theta} ) \\ \\ = \frac{( {cos \theta + sin \theta})^{2} - 1 }{sin \theta \: cos \theta} \\ \\ = \frac{2sin \theta \: cos \theta}{sin \theta \: cos \theta} \\ \\ = 2$