Question

prove that cosA/1+sinA +1+sinA/cosA =2secA
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Answer 1

Solution:

LHS = cosA/1+sinA +1+sinA/cosA

=[cos²A+(1+sinA)²]/[(1+sinA)cosA]

= (cos²A+1+sin²A+2sinA)/[(1+sinA) cosA]

=[(cos²A+sin²A)+1+2sinA]/[(1+sinA)cosA]

= ( 1+1+2sinA)/[(1+sinA)cosA]

= (2+2sinA)/[(1+sinA)cosA]

= [2(1+sinA)]/[(1+sinA)cosA]

= 2/cosA

= 2secA

= RHS

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Answer 2

Hey !

Refer the below attachment !

Thanks!