Question

(1 + cotθ − cos ecθ)(1 + tan θ + sec θ) = 2
​

Answer 1

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