Question

Factor this trig. expression:
(sinx+1)² - (sinx-1)²
Show steps.

- is there a way of factoring without knowing a2−b2=(a−b)(a+b) ?

Answer 1

It's of the form
\[a^2-b^2=(a-b)(a+b)\]
so using this here
\[(\sin x+1)² - (\sin x-1)²= (\sin x+1+\sin x-1)(\sin x+1-(\sin x-1))\]
Can you simplify the rest?

Answer 2

\[(a+b)^2 - (a-b)^2 = 4ab\]

a = sinx and b = 1

Put and solve...

Answer 3

a2−b2=(a−b)(a+b)

a = Sinx + 1, b = sinx -1

SO, [ (sinx +1) - (sinx -1)] [(sinx +1) +(sinx -1)]
[sinx +1 - sinx +1] [sinx +1 + sinx - 1]
[2] [2 sinx]

So answer would be = 4 sinx ....