Question

Which expression is equivalent to (sin x + 1)(sin x − 1)?

Answer 1

cos^2x
-cos^2
cos^2x+1
cos^2x-1
-cos^2x+1

Answer 2

Can you multiply out the given binomials?

Answer 3

Use FOIL, or the pattern (a + b)(a - b) = a^2 - b^2

Answer 4

Can you show me how to do that?

Answer 5

Let's use FOIL:

\((\sin x + 1)(\sin x - 1) \)

\( = \sin^2 x - \sin x + \sin x - 1^2\)

\( = \sin^2 x - 1\)

Ok?

Answer 6

Is the answer -cos^2x

Answer 7

Now use the identity:

\(\sin^2 x + \cos^2 x = 1\)

Subtract \(\sin^2 x \) from both sides.

What do you get?

Answer 8

No, but close.

Answer 9

-cos^2+1?

Answer 10

Instead of guessing, do this:

Take this equation, \(\sin^2 x + \cos^2 x = 1\), and subtract \(\sin^2 x\) from both sides. What do you get?

Answer 11

cos^2x-1?

Answer 12

Ok?