Question

(1-сosa)^2+(1+cosa)^2+2sin^2a

Answer 1

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Answer 2

To simplify the expression (1 - cos(a))^2 + (1 + cos(a))^2 + 2sin^2(a), we can expand and simplify each term:

Expanding the first term: (1 - cos(a))^2 = (1 - 2cos(a) + cos^2(a)) = 1 - 2cos(a) + cos^2(a)

Expanding the second term: (1 + cos(a))^2 = (1 + 2cos(a) + cos^2(a)) = 1 + 2cos(a) + cos^2(a)

Now, let's substitute these expanded forms back into the original expression:

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

We can simplify this further by combining like terms: = 2 + 2cos^2(a) + 2sin^2(a) = 2 + 2(cos^2(a) + sin^2(a))

Using the trigonometric identity cos^2(a) + sin^2(a) = 1, we can simplify the expression even more: = 2 + 2(1) = 2 + 2 = 4

Therefore, the simplified expression (1 - cos(a))^2 + (1 + cos(a))^2 + 2sin^2(a) simplifies to 4.