Question

(1+ TanA + SecA) (1 + CotA - CosecA)

Answer 1

Solution:-

$\bigstar \sf \: (1 + tan \: A + sec\:A)(1 + cot \: A \: - cosec \: A)$

$\implies \sf \: (1 + \dfrac{sin \: A}{cos \: A} + \dfrac{1}{cos \: A})(1 + \dfrac{cos \: A}{sin \: A} - \dfrac{1}{sin \: A})$

$\implies \sf \:( \dfrac{cos \: A - sin \: A + 1}{cos \:A } )( \dfrac{sin \: A + cos \:A - 1 }{sin \: A})$

$\implies \sf \dfrac{ {(sin \:A + cos \: A)}^{2} - 1 }{cos\: A \: sin\:A }$

• $\sf {sin}^{2} A + {cos}^{2} A = 1$

$\implies \sf \dfrac{1 + 2 \: sin \: A \: cos \: A - 1}{cos \:A \: sin \: A }$

$\implies \sf 2$

Therefore,

$\bigstar \sf \: (1 + tan \: A + sec\:A)(1 + cot \: A \: - cosec \: A) = 2$