Notice for any we have that,Originally Posted by mathAna1ys!5
Because the sin function is non-negative in the first two quadrants.
Now add 1 to both sides thus,
Notice that the LHS is a perfect square,
You take the square root of both sides you can do this because these expressions are non-negative thus,
You may think how did I ever come up with such a proof, well let me teach you how to do these types of problems. I first assumed that and ended up with, . But that is not a proof, thus, I worked backwards to this result.