Question

5sin4a/3cos2a если sin2a=0,6

Answer 1

$\frac{5*2sin2aco2a}{3cos2a} = \frac{10sin2a}{3} = \frac{10*0,6}{3} =10*0,2=2$

Answer 2

To simplify the expression $\frac{5\sin(4a)}{3\cos(2a)}$ given that $\sin(2a) = 0.6$, we can use trigonometric identities. First, we'll start by finding $\sin(4a)$ and $\cos(2a)$ in terms of $\sin(2a)$.

Using double angle formula for sine: $\sin(2a) = 2 \sin(a) \cos(a)$

Given that $\sin(2a) = 0.6$, we can rewrite this as: $0.6 = 2 \sin(a) \cos(a)$

Next, using double angle formula for cosine: $\cos(2a) = \cos^2(a) - \sin^2(a)$

We can use the Pythagorean identity to express $\cos^2(a)$ in terms of $\sin^2(a)$: $\cos^2(a) = 1 - \sin^2(a)$

Given that $\sin^2(a) = 0.6^2 = 0.36$, we can rewrite $\cos^2(a)$ as: $\cos^2(a) = 1 - 0.36 = 0.64$

Now, we can find $\cos(2a)$: $\cos(2a) = 0.64 - 0.36 = 0.28$

Now, let's find $\sin(4a)$ using the double angle formula for sine: $\sin(4a) = 2\sin(2a) \cos(2a)$

Substituting the values we know: $\sin(4a) = 2 \times 0.6 \times 0.28$

$\sin(4a) = 0.336$

Finally, let's simplify the given expression using the values we found: $\frac{5\sin(4a)}{3\cos(2a)} = \frac{5 \times 0.336}{3 \times 0.28}$

$\frac{1.68}{0.84} = 2$

So, the simplified expression is $2$.