Question

prove that CotA + tanA = 2cosec2A

Answer 1

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$\bold{\underline{Question-}}$


prove that CotA + tanA = 2cosec2A


$\bold{\underline{Answer-}}$


LHS = cotA + tanA


$= > \: \frac{cos \: a}{sin \: a} + \frac{sin \: a}{cos \: a} \\ \\ \\ \\ = > \frac{ {cos}^{2} a + {sin}^{2} a}{sin \: a \: cos \: a} \\ \\ \\ = > \frac{1}{sin \: a \: cos \: a} \\ \\ \\ = > \frac{2}{2sin \: a \: cos \: a} \\ \\ \\ = > \frac{2}{sin2a} \\ \\ = > 2cosec2a$