Question

Cos A/1+sin A + 1+sin A/cos A=2sec A

Answer 1

Step-by-step explanation:

let LHS,

cos A/1+sin A +1+sinA/cosA

after cross multiplication we get

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

expand(1+sinA)^2=1+sin^2+2sinA

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

cos^2A =1-sin^2A using identity

therefore

1-sin^2A+1+sin^2+2sinA/cosA(1+sinA)

2+2sinA/cosA(1+sinA)

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

2/cosA.

secA=1/cosA

2secA