Question

Дано cosa+sina=-0,5, найдите 1-3cosa×sina

Answer 1

Решение приложено к снимку:

Answer 2

To find the value of $1 - 3\cos(a) \times \sin(a)$, we can use the identity $\sin^2(a) + \cos^2(a) = 1$ and the given equation $\cos(a) + \sin(a) = -0.5$ to solve for $\cos(a)$ and $\sin(a)$. Then we can substitute these values into the expression $1 - 3\cos(a) \times \sin(a)$.

Let's start by solving for $\cos(a)$ and $\sin(a)$ using the given equation:

Given: $\cos(a) + \sin(a) = -0.5$

Let's square both sides of the equation: $(\cos(a) + \sin(a))^2 = (-0.5)^2$ $\cos^2(a) + 2\cos(a)\sin(a) + \sin^2(a) = 0.25$

Now, we can use the identity $\sin^2(a) + \cos^2(a) = 1$ to replace $\sin^2(a) + \cos^2(a)$ in the above equation: $1 + 2\cos(a)\sin(a) = 0.25$

Rearrange the equation: $2\cos(a)\sin(a) = 0.25 - 1$ $2\cos(a)\sin(a) = -0.75$

Now, we need to find the value of $\cos(a) \times \sin(a)$: $\cos(a) \times \sin(a) = \frac{-0.75}{2}$ $\cos(a) \times \sin(a) = -0.375$

Now, we can find the value of $1 - 3\cos(a) \times \sin(a)$: $1 - 3\cos(a) \times \sin(a) = 1 - 3 \times (-0.375) = 1 + 1.125 = 2.125$

So, $1 - 3\cos(a) \times \sin(a) = 2.125$.