Question

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

Answer 1

Answer:first step...

make the denominators same it becomes

[cos^2A+(1+sinA)^2]/cosA(1+sinA)

solving for the whole square..

[cos^2A + 1 + sin^2A + 2sinA]/ cosA(1+ sinA)

now as we know.. cos^2A+sin^2A =1 then substituting the same..

[1+1+2sinA] / cos A(1+sinA)

taking 2 as common from the numerator..

2(1+sinA)/ cos A (1+sinA)

now (1+sinA) will get cancelled from both the numerator and the denominator..

what remains is..

2/cosA that is 2 x 1/ cosA

and as (1/ cos A) is sec A..

the final answer is 2secA

Hence proved

hope you understood the solution