Question

Sin4a×2sin2a/sin4a+2sin²a Help! Алгебрааа

Answer 1

Ответ:tg²a

Пошаговое объяснение:

(2sin2a-sin4a)/(sin4a+2sin2a)=(2sin2a-2sin2acos2a)/(2sin2acos2a+2sin2a)=2sin2a(1-cos2a)/(2sin2a(1+cos2a))=(1-cos2a)/(1+cos2a)=(cos²a+sin²a-cos²a+sin²a)/(cos²a+sin²a+cos²a-sin²a)=2sin²a/(2cos²a)=tg²a

Answer 2

To simplify the expression $\frac{\sin(4a) \cdot 2\sin(2a)}{\sin(4a) + 2\sin^2(a)}$, you can use trigonometric identities to help you simplify it.

1. Start by using the double-angle identity $\sin(2\theta) = 2\sin(\theta)\cos(\theta)$ to rewrite $\sin(4a)$ as $2\sin(2a)\cos(2a)$. So, your expression becomes:

$\frac{2\sin(2a) \cdot 2\sin(2a)\cos(2a)}{2\sin(2a)\cos(2a) + 2\sin^2(a)}$.

2. Now, notice that both the numerator and denominator have $2\sin(2a)$ terms, which can be factored out:

$\frac{2\sin(2a) \cdot [2\sin(2a)\cos(2a)]}{2\sin(2a) \cdot [cos(2a) + \sin(a)]}$.

3. Cancel the common factor of $2\sin(2a)$ from the numerator and denominator:

$\frac{2\sin(2a)\cos(2a)}{cos(2a) + \sin(a)}$.

Now, you have simplified the expression.