Question

sinA(1+tanA)+cosA(1+cotA)=secA+cosecA​

Answer 1

sin A(1 + tanA) + cosA(1 + cotA) = sec A + cosec A

LHS

$sin \: A(1 + tan \: A) + cos \: A(1 + cot \: A)$

$sin \: A + sin \: A \:. tan \: A \: + cos \: A + cos \: A. \: cot \: A$

$sin \: A \: + \frac{ {sin}^{2}A}{cos \: A} + cos \: A \: + \frac{ {cos}^{2}A}{sin \: A}$

$\frac{ {sin}^{2}A + {cos}^{2} A }{cos \: A} + \frac{ {cos}^{2}A+ {sin}^{2} A }{sin \: A}$

$\frac{1}{cos \: A} + \frac{1}{sin \: A}$

$sec \: A \: + cosec \: A$

RHS

Hence, proved.