Question

Prove that
costheta/1-sintheta+costheta/1+sintheta= 2 sectheta

Answer 1

costheta+costheta÷(1-sintheta)(1+sintheta)
2costheta÷(1-sinsquaretheta). a square - b square equals (a+b)(a-b)

2costheta ÷ cossquaretheta. 1-sinsquaretheta

So 2 ÷ costheta.
and 1÷costheta equals sectheta
=2sectheta
hence proved

Answer 2

take a look at the answer of the answer