Question

solve this fast fast fast​

Answer 1

Simplify LHS and RHS seperately

LHS

$(coseca - sina)(seca - cosa)$

change this equation in the form of sinA and cosA only

$(\frac{1}{sina} - sina)( \frac{1}{cosa} - cosa) \\ = (\frac{1 - {sin}^{2}a }{sina}) ( \frac{1 - {cos}^{2}a }{cosa} )$

change 1-sin^2A in cos^2A and 1- cos^2A in sin^2A

$\frac{ {cos}^{2} a}{sina} \times \frac{ {sin}^{2}a }{cosa} = cosa.sina$

LHS=cosA.sinA

RHS

$\frac{1}{tana + cota} = \frac{1}{ \frac{sina}{cosa} + \frac{cosa}{sina} } \\ = \frac{cosa.sina}{ {sin}^{2} a+ {cos}^{2} a} = cosa.sina$

RHS=cosA.sinA

LHS=RHS

Hence proved