Question

Find the value of (1+cot thita-cose thita)(1+tan thita+sec thita)

Answer 1

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