How do you verify: #sqrt(1+sin x)-sqrt(1-sin x) =2*sin(x/2)# ?
#sqrt(1+sin x)-sqrt(1-sin x) =2*sin(x/2)#
2 Answers
One cannot verify
Explanation:
I shall show that
Both sides of an identity must be equal for all real values of x; this is clearly NOT an identity.
This is valid for
Explanation:
We know
Thus
and
The subtlety here is that when we take the square root, we have to take the positive square root. When
so that
For the other square root, note that for
Thus
So, finally