Question

Simplify square root of (1-sin theta)(1+sin theta)

Answer 1

Recall the important identities:

i) $(a-b)(a+b)= a^{2}- b^{2}$, the difference of squares formula.

ii) $sin^{2} x+cos^{2}x=1$, for any angle x.

Then,

from i)

$\sqrt{(1-sin(theta))(1+sin(theta))}= \sqrt{1- sin^{2}(theta) }$

then, from ii), we have 

$\sqrt{1- sin^{2}(theta) }= \sqrt{cos^{2}(theta) }=cos(theta)$


Answer: cos(theta)