Question

Simplify (1 − sin x)(1 + sin x).
A) 1
B) cos2 x
C) sin2 x
D) tan2 x

Answer 1

Simplify (1 − sin x)(1 + sin x).

Answer:

B - cos2 x

Answer 2

Answer: optiob B.

Explanation:

Remember that:

`cos^2x+sin^2x=1`

Then, having the expression
`(1-sinx)(1+sinx)`, apply distributive property. Then:

`=1+sinx-sinx-sin^2x`

Now you need to add the like terms:

`=1-sin^2x`

If you solve for
`cos^2x` from
`cos^2x+sin^2x=1`, you get:
`cos^2x=1-sin^2x`. Therefore the answer is:

`=cos^2x`