Simplify (1 − sin x)(1 + sin x).

Question

luigi0210 · Answer

FOIL it out.

luigi0210 · Answer

If you do it right, it'll give you a trig identity

anonymous · Answer

Use (a-b)(a+b) = a^2-b^2

and sin^2 + cos^2 = 1 ?

anonymous · Answer

(1- sin x)^2

anonymous · Answer

that is what I got...

anonymous · Answer

(a-b)(a+b) does not equal (a-b)^2

anonymous · Answer

1^2 - sin x ^2 which is 1 - sin x ^2 which is what I got when I FOILED it...

johnweldon1993 · Answer

Well correct but remember it will be

$$\large 1^2 - sin^2(x)$$

so what is 

$$\large 1 - \sin^2(x) = \space ?$$

johnweldon1993 · Answer

Hint would be to remember the identity

$$\large \cos^2(x) + \sin^2(x) = 1$$

anonymous · Answer

Yes, I actually have that identity written down. But I am not sure how they tie in together in this problem.

johnweldon1993 · Answer

Well...if

$$\large cos^2(x) + sin^2(x) = 1$$

what would happen if you subtracted $\large sin^2(x)$ from both sides?

$$\large 1 - sin^2(x) = cos^2(x)$$

anonymous · Answer

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

anonymous · Answer

And you already wrote that... whoopsies.

anonymous · Answer

But then what?

johnweldon1993 · Answer

That would be your answer...

What you had was to simplify

$$\large 1 - sin^2(x)$$

Well we just saw that

$$\large 1 - sin^2(x) = cos^2(x)$$

so your simplification will be $\large cos^2(x)$

anonymous · Answer

Oh... okay. I feel really unintelligent at the moment. THANKS!

johnweldon1993 · Answer

Don't worry about it, you're very intelligent :) and anytime!