Question

prove cosA/1+sinA+1+sinA/cosA=2secA​

Answer 1

Answer:

Here is the answer

Step-by-step explanation:

Given cosA/(1+sinA) +(1+sinA)/cosA

On taking the LCM we get,

={cos²A +(1+sinA)²}/cosA.(1+sinA)

Combining the like terms and adding and also we know that,use sin²A+cos²A =1

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

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

=2/cosA

=2secA

Hence Proved

Answer 2

LHS =cosA/(1+sinA) +(1+sinA)/cosA

={cos²A +(1+sinA)²}/cosA.(1+sinA)

={cos²A+1+sin²A+2sinA}/cosA.(1+sinA)

use sin²∅ +cos²∅ =1

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

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

=2/cosA

=2secA = RHS

$\huge \pink {SsR}$