Question

Упростить cos (60+a)*cos(60-a)+sin^2a a - это альфа СРОЧНО

Answer 1

cos (60+α)*cos(60-α)+sin^2α=(cos60°cosα-sin60°sinα)*(cos60°cosα+sin60°sinα)+sin²α=(cos²60°cos²α-sin²60°sin²α)+sin²α=

(1/4)cos²α-(3/4)sin²α+sin²α=(1/4)(cos²α+sin²α)=(1/4)*1=0.25

Answer 2

Simplifying cos(60+a)*cos(60-a)+sin^2a+a

To simplify the expression cos(60+a) * cos(60-a) + sin^2(a) + a, we can use trigonometric identities to break down the expression. Let's start by simplifying each term individually.

1. cos(60+a) * cos(60-a): - We can use the identity cos(A) * cos(B) = (1/2) * [cos(A-B) + cos(A+B)] to simplify this term.

Applying the identity: - cos(60+a) * cos(60-a) = (1/2) * [cos((60+a)-(60-a)) + cos((60+a)+(60-a))] - cos(60+a) * cos(60-a) = (1/2) * [cos(2a) + cos(120)]

We'll keep this result in mind for later use.

2. sin^2(a): - Using the identity sin^2(a) = 1 - cos^2(a), we can simplify this term.

Applying the identity: - sin^2(a) = 1 - cos^2(a)

3. a: - This term remains as it is.

Now, let's combine the simplified terms.

Final Simplification

We can now substitute the simplified expressions back into the original equation and simplify further.

Substituting the simplified expressions: - (1/2) * [cos(2a) + cos(120)] + (1 - cos^2(a)) + a

We can further simplify the expression by using the value of cos(120) and cos^2(a).

Conclusion

The final simplified expression is: - (1/2) * [cos(2a) - 1] + 1 - cos^2(a) + a

This is the simplified form of the given expression cos(60+a) * cos(60-a) + sin^2(a) + a.