Question

2sina+√3. 2cosa-1 ________ = _______1+2cosa. √3-2sinaрешите пожалуйста очень прошу

Answer 1

(2sina+√3)(√3-2sina)=
(1+2cosa)(2cosa-1)
3-4sin^2(a)=4cos^2(a)-1
-4(sin^2(a)+cos^2(a))=-4
-4=-4

Answer 2

Solving the Trigonometric Expression

To solve the given trigonometric expression 2sinα√3 + 2cosα - 1, we can use trigonometric identities to simplify it.

First, let's express 2sinα√3 in terms of cosine using the identity sin(α) = cos(90° - α).

So, 2sinα√3 becomes 2cos(90° - α)√3.

Now, we can rewrite the expression as 2cos(90° - α)√3 + 2cosα - 1.

Using the identity cos(90° - α) = sin(α), the expression becomes 2sinα√3 + 2cosα - 1.

This means that the given expression is equivalent to 2sinα√3 + 2cosα - 1.

Therefore, the expression remains unchanged.

Conclusion

The given trigonometric expression 2sinα√3 + 2cosα - 1 remains unchanged and is equal to 2sinα√3 + 2cosα - 1.

If you have any further questions or need additional assistance, feel free to ask!