Question

Cos a /1- sin a + 1+ sina / cosa = 2seca

Answer 1

I guess the question is how to prove the following LHS equal to 2seca+2tana...

Answer 2

Answer:

$\frac{cosa}{1 + sina} + \frac{1 + sina}{cosa} \\ \\ = \frac{ {cos}^{2}a + ( {1 + sina})^{2} }{(1 + sina)cosa} \\ \\ = \frac{ {cos}^{2}a + 1 + {sin}^{2} a + 2sina }{(1 + sina)cosa} \\ \\ = \frac{2 + 2sina}{(1 + sina)cosa} \\ \\ = \frac{2}{cosa} \\ \\ = 2seca$