Recall the important identities:
i) [tex](a-b)(a+b)= a^{2}- b^{2} [/tex], the difference of squares formula.
ii) [tex]sin^{2} x+cos^{2}x=1[/tex], for any angle x.
Then,
from i)
[tex] \sqrt{(1-sin(theta))(1+sin(theta))}= \sqrt{1- sin^{2}(theta) } [/tex]
then, from ii), we have
[tex]\sqrt{1- sin^{2}(theta) }= \sqrt{cos^{2}(theta) }=cos(theta) [/tex]
Answer: cos(theta)
