Question

Simplify expression

(1+cos a)(1-cos(-a))

Answer 1

Answer:


(1 + cos a)(1 - cos(-a)) = sin²a

Explanation:

Using the even property of cosine, we can simplify cos(-a) to cos(a):

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

Using the formula for the difference of two squares, we can simplify further:

(1 + cos a)(1 - cos a) = 1 - cos²a

Finally, using the identity cos²a + sin²a = 1, we can substitute sin²a for 1 - cos²a:

1 - cos²a = sin²a

Therefore, the simplified expression is:

(1 + cos a)(1 - cos(-a)) = sin²a