Question

(sec A-cos A) (cot A + tan A)
=tan A sec A.​

Answer 1

Step-by-step explanation:

LHS-

= (secA - cosA)(cotA + tanA)

{we know that, secA = 1/cosA, cotA = 1/tanA }

$( \frac{1}{ \cos(a) } - \cos(a) )( \frac{1}{ \tan(a) +} + \tan(a) )$

$( \frac{1 - { \cos(a) }^{2} }{ \cos(a) } )( \frac{1 + { \tan(a) }^{2} }{ \tan(a) } )$

= (sin²A/cosA)(cosec²A/tanA)

= tanA × secA

= RHS

cheers!