Which expression is equivalent to (sin x + 1)(sin x - 1)?
cos²x
-cos²x
cos²x + 1
cos²x - 1
-cos²x + 1

Solution:

Given expression (sinx + 1)(sinx - 1)

This is in the form (a + b)(a - b), which we can rewrite as difference of squares: a² - b²

Here a = sinx and b = 1

(sinx + 1)(sinx - 1) = sin²x - 1²

= sin²x - 1 --- [a]

We have a trigonometry identity sin²x + cos²x = 1;

⇒ sin²x - 1 = -cos²x

Put -cos²x in [a]

(sinx + 1)(sinx - 1) = -cos²x

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

Summary:

-cos²x expression is equivalent to (sin x + 1)(sin x - 1).