Verify that (sinacosa)/(1 + cosa) - (sina)/(1 - cosa) = -(cotacosa + csca)

    refresh if you are seeing weird display errors such as \begin{aligned}, etc.======focusing on the left-hand side:     one strategy is that, if you see a summation or difference of fractions, try to rewrite it as a single fraction. we see that happening on the left side.make the fractions have a common denominator to subtract those fractions.multiply numerator and denominator of by  to get    distribute and you get    multiply the numerator and denominator of  by  to get    distribute sin a    combining these fractions:     combine like terms:   and  cancel each other out.    factor  out of the numerator.    expand out the denominator    the denom. looks like a variation of the pyth. identity.if we have  , subtracting both sides by  gets us  , hence    ======focusing on the right-hand side:     another strategy: we can rewrite everything in terms of sine and cosine.since  and  , we have    they have the same numerator; we can combine the fractions.   

16 minutes is correct

)because it's going in order of the math sign