Question

(1+cos a)(1- cos a) ​

Answer 1

Ответ:

Пошаговое объяснение:

(1+cos a)(1- cos a) ​= 1 - $cos^{2}a$=$sin^{2}a$

Answer 2

To simplify the expression (1 + cos(a))(1 - cos(a)), you can use the difference of squares identity, which states that (a + b)(a - b) = a^2 - b^2. In this case, let a = 1 and b = cos(a):

(1 + cos(a))(1 - cos(a)) = 1^2 - (cos(a))^2

Now, recall the trigonometric identity: cos^2(a) + sin^2(a) = 1. You can rearrange it to get sin^2(a) = 1 - cos^2(a). Substitute this into the expression:

1^2 - (cos(a))^2 = 1 - (1 - sin^2(a)) = 1 - 1 + sin^2(a) = sin^2(a)

So, (1 + cos(a))(1 - cos(a)) simplifies to sin^2(a).