(i)prove that 1/1+sintheta +1/1-sin theta=2sec^2 theta

Question

(ii)prove that cos theta/1-sin theta =1+sin theta/cos theta

Answer 1

1 / ( 1 + sin theta ) + 1 / ( 1 - sin theta =

( 1 + sin theta + 1 - sin theta ) / [ ( 1 + sin theta ) * ( 1 - sin theta ) ] =

2 / ( 1 - sin ^ 2 theta ) =

2 / ( cos ^ 2 theta ) =

2 sec ^ 2 theta