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)


`√((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)