Question

Prove that : sinA/1+cosA + 1+cosA/sinA=2cosecA​

Answer 1

Explanation:

`(sinA)/(1+cosA) +(1+cos)/(sinA) =2cosec\\\\\\(sin^(2)A+(1+cos)^(2) )/(sinA(1+cosA)) \\\\`

`(sin^(2)A+1+cos^(2)+2cos)/(sinA(1+cosA)) \\\\` and we have
`sin^(2)+cos^(2) =1`

so
`(1+1+2cosA )/(sinA(1+cosA)) \\\\`

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

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

`(2)/(sinA)` we have
`(1)/(sin)=cosec\\`

Finally
`2cosecA`

I really hope this helps coz it took much time