How do you prove: #cos (x)/(1+sin (x)) + (1+sin (x))/cos (x) = 2 sec (x)#?
Let's take the first member:
First of all, the equality is possible only if
The corresponding conditions on an angle
Let's try to simplify it in straight forward fashion.
First, bring the left part to a common denominator:
Transform the numerator, leave the denominator:
Therefore, our expression looks like
We can safely reduce the last fraction by