Question

cosA/1+sinA. + cosA/ 1+ sinA =2secA

Answer 1

LHS = cos / 1 - sin A  + cos / 1 + sinA

LHS  =  cos ( 1 /1 - sinA + 1 / 1 + sin A )

LHS = cos  {  1 + sin A + 1 - sin A  / ( 1 - sinA )( 1 + sinA )

LHS = cos ( 2 / 1 - sin²A )

LHS = cos ( 2 / cos²A)                                     - (∵ 1 - sin²A  = cos²A)

LHS = 2 × 1 / cosA

LHS = 2sec  =RHS                                                       - (1 / cosA = sinA)

HENCE PROVED

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Answer 2

$\bold{\huge{\underline{\underline{\rm{Explanation:}}}}}$

Refer to the Attachment^^°