Question

(1+tanA+secA)(1+cotA-cosecA)​

Answer 1

Given : (1 + tanA + secA)(1 + cotA - cosecA)

Solution :

$\implies\mathtt{( \frac{sin \: a}{cos \: a} + \frac{1}{cos \: a} )( 1 + \frac{cos \: a}{sin \: a} - \frac{1}{sin \: a} ) } \\ \\ \\ \implies\mathtt{( \frac{cos \: a + sin \: a \: + 1}{cos \: a}) ( \frac{sin \: a + cos \: a - 1}{sin \: a}) } \\ \\ \\ \implies\mathtt{ \frac{(sin \: a + cos \: a)^{2} - {1}^{2} }{sin \: a \times cos \: a} } \\ \\ \\ \implies\mathtt{ \frac{{sin}^{2} \: a + {cos}^{2} \: a + 2sin \: a \times cos \: a - 1}{sin \: a \times cos \: a} } \\ \\ \\ \implies\mathtt{ \frac{1 + 2sin \: a \times cos \: a - 1}{sin \: a \times cos \: a} } \\ \\ \\ \implies\mathtt{ \frac{2sin \: a \times cos \: a}{sin \: a \times cos \: a} } \\ \\ \\ \implies\mathtt{2 \: ans}$