Question

cosa/1-sina +1- sin a/cosa = 2 seca​

Answer 1

Answer:

Answer

LHS=

1−sinA

cosA

+

1+sinA

cosA

=

(1−sin

2

A)

cosA(1+sinA+1−sinA)

=

cos

2

A

2cosA

=

cosA

2

=2secA=RHS

Hence proved.

Answer 2

Answer:

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