Verify that seca + tana = (cos)/(1-sina)

Refresh if you see display errors such as \begin{aligned}, etc.======focusing  on the left-hand side    one strategy is to rewrite everything in terms of sine and cosine.since and  , we have    they have the same denominator, which is why i am able to combine them.that looks as simple as simple gets. can leave it alone. (read the remark at the end, because there are things you can do here, too.)======focusing  on the right-hand side    in this situation, there is one strategy we can use: multiplication by the conjugate.for the right hand side, the conjugate of  is  . we can multiply the numerator and denominator of the right hand side by this conjugate.why do this? because it will produce a difference of squares in the denominator, which may permit us to use a pythagorean identity.(another rationale is that, if you look on the left side, we have 1+sina; this can lead to you conclude that we need to multiply by 1+sina on the right side to get it there as well.)    the denominator is a difference of squares expansion, in the form of  . doing this to the denominator gets us    the denominator is a variation of the pyth. identity.with  , subtracting both sides by  gets us  . hence    the cosines (partially) cancel out and we are left with    ======you could have also did the conjugate step for the left-hand side when you finished simplifying it all. there are usually many ways to prove an identity.i hope i'm not doing your entire homework packet or something like that (though i do understand that this one involves something different than the other questions you've posted)